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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="author" content="Liam Damewood" />
<title>Quiz 2</title>
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xaXpygKB5dWVlFrb5mQOydwB7i0J6ubFjh7npdh1XXdKUdEAmoj3W5Db4m4QE1LVCapO1XgH2D%2FkB08JF83SNM9ZhZf5I9%2B7Rz8J%2FI3IIfrMb5LHcjByu%2BUvGUKxQ%2FkcaLYdZ40f8JWOkw%2BA4iEBtlYSmddP1HFw%2FdKtShd1YQrncW61ZeqsIAcmYleEIEKAhx1ry8ND6aFh%2F8V9VHtiPdBPGObFcRVTzQgcz40RO7WEpW0ba3k2z3i6zBvlL9xO4ka%2F1EVnLTSa%2Buo%2BmkNzrwWDyPcz4lWOAxAp2%2BTrKORXoPGvm6d5aKpzt50u4573rAOfhP1CUXfpbjl36l4XWpysmXBCr6PbGqqsTnSRvReJFj4Xl9rvYfHFko%2FqPrb9YYEpV1CsKxTiSrXhisap%2F%2BC%2B6uu%2F8CZVz1iWlY7fGdnKxd2eM7WS2lcof2ANfjrBHRsoomvoE%2BuiF%2FpXpsCFnJYVZIVk7UsM85PYeLXYofPYf9H42YsMdtUq%2FMTd79Ho4bf2S7Gq9PVRxDC6lKG1VpVBV9cvFXGr6oVycSFZ%2FauXWquCnKooTpFvcfy0YiWVX%2BI%2FD8UOPXvp%2BE5%2Bom3JHt0IXP6MxS5U%2FAqovYd3l62%2BltAxkkq6q7T7LR3xT%2Bcz8gICtekEZU28Hq3d9JkEXhcfclufMmmZusgqh%2B5ww%2B7k3Vwcd9XbHh1JbiELt3Fu67QYbvmRs%2FCg5by%2Fr3TnRlZXhu7ijl5o6qlZ%2BrQrpkGp3PTVTZFKpwyqWabnH%2Fce5T6T%2Ba%2BNhiV5b7vOiQWG1XNvGNzngqewJWX%2BO7%2BPupIVbDas6n8HPju1ZMXmrvkcJ%2FhQ1Ya89RaqlV9P%2Bu0DacBdfrcx5rlPXMqW5%2B%2FVv8cfLHuP4t%2F6ZgDdhPFR8DGRmRoMk6R6Yc9MgU65TdN%2BKH32y1gyJruJn9x3%2BQ4%2B1zUvkZZYoyqq52HfJR1T3OUca8Ss9VrVhgoR1nngEaUXl%2BEwnEj%2B5Lg7fIsNx%2FsEWwXdT%2BI%2FD8UOO75zqXdKad2WS2XFS9L3XHH%2FH3m9r4nePnO%2F7Ys%2Fk6qErLYy0lJ6agZeeN%2FwwccYGT1QoEPwJqvCIveWiGhaw0jqw4olppFhqa8b%2FC%2BdTSMfJ8SlX%2Fp%2B918A8%2Bor5fxP%2FNTuvM3TtoeHe%2FThlVC9NKslFVNwNc6blq86mEHcyuYlSiOqOvmLPKAkLhPzbxCP6j62%2B9f0qwwjHOiiWI80kKVVktH0mD79lpNHuEPZ9yx6Q3iKpAKUiIS%2BdKK4ZmEpg0z1gZ%2FjhD12TDPydq2A6DMfTF%2FCCSlRZO0fLXPJsLM9o5%2FJ%2BS1UU8jHffrIaAVo2H93qXRX3g%2FV5fZeaqtAxwpeeqH3Trtr4z%2Boo5qyzjqus%2FuvixZ5JszVn3T9bAuDz2jM54qngC1XyGupJhFtiO%2BapVZZeFqvBG9bLT64cJ8zEW2juBk3sMRUbTMA9ggQX%2FxuNExVKRpvwrklXWFA5ZaUTl2d%2FRNOseP4pZYB18QoGHvnMyyNx5aXCbSf9x47s%2BV9Vv%2FQ2nBFacueFU%2BfxH298aemcj%2BAollosRz0QwI9ygM56qmBNbdKZpA5nYorobKAtV1yzEXc4xMjWQ2Xzu%2BE7FzK0BZnfYN3ezIOaa7cYL%2BL91Kw6%2BwooX2cJdqES1Yl3fwkumIJzZeGJX6gvVmzcdfOOV0JL6h1jjlZuVAa78e1Xd1scYiWP5mRhHlc9%2F9PFYhwhrwqz%2BfBOLKP8AaClJVcxhKRb%2FbHAgM5D5bBD67tR1UFX8XUSS8JcpqS8QN340V4kWuHQHNRnlvBhKfbH7Vr8H6fkKWPUwq6eGeuYgy1ZNqcPGOz6%2BR9SZ1V7of6CvfPi4Z0Y6zuSjamFa6bv2XhUpNzRDI2ruGXdyLNC1U%2FVs9fxHH4912DsxkOnMds9tPgd%2FPNEpvw99qvKrPL3r8FZaC3Vl26BE558ratV5h5brrxqrSjZWe2oL%2FbGSS62BPrSGWgP31eFR1ZYP7%2F23Jv5tWjqelgG%2BMe9VoU1C5X6i5fIfCh7GYRjtwIM65C%2FhnJc6S%2F9XnldPHdKgJoWtn6q6WQa0qq4yZuwG%2BY%2FxN2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYseVnpcgqGjNm7EYTNd1MEGK0kaUITo7BMiNUZj1D6RBgIRmWfxAO%2FFpHr1Vl6qOHh2WCxTJWwxWpzzycMW1rU6TJ5QMexTRpz5cqLpp7Tvw4WJlhBGp%2BBo7p79qA4m5Bmngs%2F5fXJWZFOsN86VmYRFb3agsKnuuswqLabGc2wig6q2t%2BjKX3TfZN4tc1P6Y0CV1XT7c%2Buvjor4tXpcgXo5daH5QVaUf8fJhRy0f8ShZltOdLW1lj1bW5cG1qRVxmL77HjjgmvE9R%2FzPNIBmL4pz2%2FS4zGXS56nQyJ70tVuA43%2FnhhXCDWLVTsHLHWSNKIav78VHwuOp%2FIIMipCx1YtdARq2zGvoUS986vnXcXu35aXmpqlsfXTwuQ3eviwCdg68rVx9cjSm%2F72K8qp0Ka69yLaEXBOWD7i5NogZ0pBfagNRNqJFxxsqEFfWPwLL%2B09uwHqe3jaYjJJ1eWCSe0SKcjaeJvbvxVmCVVIo0mRsZbeHSfvd3JVC1cDG3mnyFKyZVeNRZBYmKOKvFKsJysjg6o%2BzmrAAX9OBrN1HQg9KAVKq66wPik8r6uPCT1iQBH4jbAtCO9c7Gmb8KgVM%2BfqdTH%2Fyu9bWEasxz4a06Nd5xLnewJl9aLgT0WD2Vqon8Ot6IYncG62CUwRrSIF%2FgCGtkgnsnosow2zrYZMcO3HPU%2FiPwqxhxq40cvmkhMjI00%2FaV%2FG5xiVySOYQtkapLVRdU5HNTVb3sG3VWD28VlUA7vFWus3rbPl76oT28l06y2%2FaVj6ru%2BnC8vD4Cb%2FWFUMG%2FT4XH2hcKkKBASfsT6vpA4Buj1ydHk5BqNakbb68qVa4%2BFe7kXqsqkWWbd4sS5D7Nq8qnh9fhq6ASUbCGlDUMzYSvyueGPCTnI541tkrS2bvxqGrS9jZl7inw218N%2Fe75%2B2RdsdMygrCWQjrAh6pe8igqsjo4SsrB0VkV1VPprIau8tLvS92Xk%2BgMXVU0X8ZyaqQIe9z14TWS14fjYceRL%2B1585dWnQL%2FP5PsR790%2F%2BRHvwQRrA%2FU9YliQHhQVZ%2FkNwJPM6d8qumNqgkP%2F0mw8lE1zh7dUfyzR3fECSoZKDuzd6IZZrcwKtdQ8FVVjzwQWaTGlIj%2F8bZ2hrK8%2FmKhznTC9jV7MiHrLH2pir3s0qaWj5Q6KQe3zmoyT2uZzqoVE5InEAzWijBJLnFcKMQlb2pRH8sWpuLEltWH42E86rbr1I2LlGV43EFndIv7J6NbZDvXuNsHHvmrqvpgcshjZLvsG56mlmoIoIpQuUZV3SSUF1VlSr1JNtlU%2FLPJJlp9qqruehS%2F3vUolXr3DHZmdah6zyC%2Fm3sGfdu%2F353R5d2ebHiTzlX1GloX7%2Bisiscu11nlsp9izM7nFX8lu4aOEJeoD253wLdAkNfHqb%2B4Uzne1nzFunMl2j7LFl%2F1byOn%2FJ452FykRVV%2B%2FwUv3dqB93QSKHKdW71RtRSqWnUDmQP7T287sJ%2FL6B3bIU1yVbtd284wVNPqYwVwRMWR1T8ALqz12mMbzupQde2xzeesGEaAsoCZ%2B7I7D5y8HqqKTF%2B5qaqrs4r5U97TYn24Ui%2BMSl%2FL5w4rGd%2FUaKUyJBf1YbWjaZALrVXVx6m%2FuFM5Pr%2BN0IR9NxOqNnLKB6m1enX53u354H7lm700rf1vxKgKMUqcrYAU0Qq1jF6xzJjjwH6jGB6jaR4AQ964gTXA%2FzUUPFDv2r6dcu8vxEe%2BHv9Z62vgq7WUlzWibUsKgIsTMuWnqp7OqjUswt%2FeP%2FExJx8CD9Nqw5NRlPrAcBdU67668PbGCiq8837RST9I1ded8qspOrT6urVcqfn5%2B%2Bj4So%2BqOjPn0bQXVUcVbylY8MQuzMOLvLHqKgJ%2Faotc974YP33f44mOxUd%2BQXtZI8ZXERIvM6rq6ay2vyHKvOOP%2BD3f70P2ZwTFdQkq1P71dV%2F18N6uK6tRZeuDNcJ3rzr4ys9V6Ybqy0upij9VnFeLGzFqXMfGUzUvHTyrAXo3UF7W8PeqPBMsU6QUvxVqiFVVOPzcEKrq6Kx2LIoyh1%2FG74dfFt%2F7adrru4qu7qseXp%2BqpdYHE1IDGTUeXnak9k5sPkfXuV36Z4X%2B9Xf2vHMO%2BW4LelR1Tz2KPy8Pk9Pb%2FXrGsmM%2B2v4Gzp8YYrYjN9a7Y2eS5mu%2F%2Ft6bVJ1VlwJqkPepKi1UPRVd3fro43V1fa%2BjPt2o2k7QrQ3Z%2BA4dnVsNXeKUBzolL1%2BbDK7rU%2Fd6XTZELtRtroeDrMTsRDdVxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjBeb6o%2By0Pt5KEzRo61BQha4rq6dBmzsnnUdfrlhLodptTKuFmDVJLn0sd0ZGdafebSRTli2lRY0tO8OVCkMzSS0VYAfPQuvfUp3VeDG%2BiNKTVLFK3ZU7aM6KnDijC0TqWfiqSo2CGxdvO7TnwP7e2RBZwpo1jB9Nss3n5Eu3rMmwTX%2BdtTuaqr4lULqUjgBkOUvuaJT4gG7ntEQYW3qvxWdWaOgsrn8SpSdDAxm6CnAhXk3WKLNXSzKqWKU%2BVVGCxCXi9rBegxCbcDgJy73WXiOQzpbYhBUUKy5Al9TxZ%2BpD6nolyZQaBC1QcgsKloK4S79Y%2F4gKvIWCpm7TwRa3Pr271z2L1ZTe0ajwxWVTFnZSl9cVo5JMl3qq8r3WNSU5VVFTIKKhAlyMV5HVq9nKS9X2J9xomXApF8O0Ckq3lHKYaKHfDZ7unU0wykYMos4oZh1fpFI18QcvyS8vpwJH7%2BQrGPOqi%2FX%2Bo7EOtngJHDEi6L%2F%2Bs6hlU%2FD6CzWFkAqt1jpU9fZmf77wPSuKNxTJURXJp6cCXIyXk7WyVEWioaCnc%2FzgvKzvcsbf3lmuczj6G5UcJoZr7ez5%2B7b%2FraojcFPVijWdBE3gs1SqYquqRNyKW05noTVR0lxzxxrtADVQQkBb8QA4yaiRVjGqFKqipK%2BsJvamNFdzeR5bmse%2BCp930lWAvfEyslaWqrbu7DcFwcI3lIBq78TU0NTQ3olkXn5ZZrftQ6mrX4LAaDthLszH6iaGTa4KaZ0gHqcWFMJVlqq6Gha6AapXcHpzA2A%2B9y%2FWIqTUJ0%2FySZ324drbsueLHBt5BYmKm4AEFqw6G89CemT1w%2FuTtfJUjRf0n3HCo%2B%2BdPdC5iq1iBzqFgrAi%2FL26%2BW2rL74B0S0vUNwd91fBRFHzx7TNkOL%2FNcnu%2Fh83n6q6Ghb6qhf6AW3lAmD0F0j9pR0lQZ3a81a10iHJSLzUm9e%2FpRIXtfdACCJRo7YAeuPFHN6LfOvfklTWB7%2F%2BLe%2BzKk9V%2FV66%2B9KmNvy6qa37EiHI7otDd4QCa9F8aKImBUhkNY5MRVngeRKRjifZxqM3n6olvSrTPEMnQK1sAIyEG5liIXcATLtXVxooBCX40ttDEN%2FmjzQUr4MXg4Hm%2B6O5M1y7%2BhSTD4SzpPvQeOGt9Pq3vM8qjaq9s6e3UUa80qgahTzx6W2nt4UfjhK6g9DfgxxnP9%2BJzB7D%2B6ikuB8SXrEPKUSKfYZ731WOqtaYHXyNUQitm8%2FVPUMnQK18AIwZdXcATLvXglGwRa89kT%2F%2BeCvWeKUNIr7b%2Fpdn%2Fd3kUxHVC%2B9P1NKoauvk14gNLtTBZnFqW%2F3om1ngo8BHzaT9Q8Ps4eeEk20%2BB3vo%2FD0prRSwxlqvJdmdv6dQCbuMB%2FoqR9Xm3F3rB8CVyAAvlwC4OANMFwHUzQB3gbokPzh%2F%2FPFNuSlcxK%2BrEeSjELUYLyOqN1WHZmQ3Jza0EBtcEGgx7wp2AkmSGGaURUlymJjHPZB%2FvTH4d%2FbcXPJXS9YenlZaBcRIEBNL%2FJxn%2FlqJg82hnSQGbaTkeLeLydIgJQWcyw1%2F3Rlgan3UVHVUHIGB9lFKWq%2FoKkg%2BKlHdeGtMRlS%2FEMAf7955hpNV1RTFfwKhLYYpkcO0DmK%2BrmlBqNnzfHFgwb9GrQUbJ8GfH9QrCZjh5zReUbZ5C7R4i85IKZIe7iPEdF6tlT9AXV4ZYEHVUupTiqpxGahqZ55COsVyPGjMhsoZUhVuEYUC1cp61BaU31DOpsspEafyWxUrlW4L6tJN2VgB%2Fkghh6a0uX8w5o3nSQ%2F3gYmUcgacyw2v73NLz6HVpxRV41Iy8MtUCVj9ZwDGtNqzRf0TY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8aMGTNmzJgxY8ZujsFqucCyqMe0eRbGjEmI2nhR%2FHG6FDdmTYPuyzRFFsxGn7Euw%2FqXMzQ8LucGaZThkjub4WXQkmmasrIxYyU5%2Bbrm7ksJ6coR7obNoDIUgX%2FNSo1DlOxuxtV32QT8D%2FgMRcKk%2BWOQRvmKgrSGoRNgjuA1djarJcu%2FXfgzuKpUq%2Fx57MRgjX6dmqhhorKyW1sW20ofqz5LDw%2F327dsPDLvLTS%2FWYrnS%2BJoZ1GwrvZM08R4nFand95Qtux%2B0ckDH00N9c6mvpCPkbgwbCAzmsaF1mHFiklUiBnIgGh3SqwTbbyorOjBqK2ZFHhJTaTVuaW4fJ2rVTd4y4ZTvbN%2BMp0C35UdP4prB1cxaw%2Bl%2FL0TQzNd2eM7Wa2VblPeAZe60pFBF%2B0fZbpYyll6%2BDgsJ4J4iTwNEms3SxV4kZ2D3sJd1vkks6V4viSOdhYF67RnmFQjd%2FuTO2%2FwH8n98sJACwjIeqFfVtDa923hbnyiHUjWte%2FLaB3l2FpnLV5UQW6rry2HDCmD4JavQB40nVsq1Dl4S%2BPFxovn1sGysmoFPsUaISwHAaxWdMs6Zfmw1A%2BXwnESbjglb2gUssrpU4QoMuhcUYfLXulhaWfp4fEa7bhGl7gzgLN2s1RVRBlWuGySUcjqhaesV6Vj3e0ZJZJV4OWqZY5xqTSf0p3Cui%2FtvlW%2BEA2lJIZf5p9RFSHC5LQ%2BvLX4EcnVdNd86SDXLMibAkc8FnTfQ%2FelwVvUeFRYbWZ87AO3PKnET9qhr01U2QJ8KHc6zNzjX1jaFQik0%2F5qN3ewtLN08bzlEyC7CkFY382mqnDZJIkaXnhaq1Kx7vakkdXB62qseJTuFObWYPAzFD0R4l6xD%2FEcf2xssSvLl2W7H1HiG9k4HGc4VguHkSv%2BOU3L7wHrL6OqwAeejwCWb%2BgxNHNunWIUmwyhHut0WNncjRfbc4r9yfzXdkXAbCtAXIySZbgcLOUst2PRruI8pyiGwmn1SFZZqnKXpVHDC08VN6Nh3e1JqZE%2BUSVk1SNqVdWGs3w7DEiv2FtiyMLB7rnOrMcjysrG4aEZHKvzAixX6XM3TlQZMQR%2B3dTpbRAmx7uyeycgXK2W45%2B%2BtwuSYu1CS0oSvm845SW3IQ%2BYhYAklapRl5uoz2o6qYcvplJYKSRTeaoW3rN%2FDOSNp%2BsQUrCFRFVnX0T7g%2Bi7psZKz1zR%2FeoStapq306uqNaWU1U7frc%2FtvdPibxomHNz%2FRdk4fXGo32TDjbOKFQNPBbN1V%2BeNMnv3BJiNfj11BbWIKNeTguq9vhOjCU4UWVqRrw3dG%2FnpO5NedvTqepgKWedW6eHL6bS0MzH99x8qrrvwT8G8sbTqUrB5uV13Eenuv3jTO%2FlnZWOF94vfz2jQ1TcoGhkymlmSLrU%2BGPHnoH55tniRzT2jCy87vjz4fWOsmCSRNWew3sneP2jykdfcC81%2BOKJQG0gK9ckalbUSKi8ijPVYQ8ihZAqxakcLOUsoftIv0rSta8PyLiFVF5ReaqibyZJw4kXnkpVGlZ3Vx%2Bn%2FcNM52VNuPh%2BA4%2Fx1zN0oqK9kxCPHLK7QanjNvTO2sFyzN13yaTKNpyNstW%2F7b8g0PKdXDBIwEwlTKoaWDXqkmOoocbnk0CgSEjDgwRai7p8Tlbcyys3V02rwx57%2FK2mqB4XY2ln6eKF4Cq8zuqkyLhVmqrcN2nDiReeGqvQsXqKiPpk9SAqzAw%2FFa9ndOTHWPWR7Tju9cydT6mwWM0I7rA67%2FRdMvzJjV3ZcF6wuCsr8sc%2BwfgTuEGU6NtW2ptF7Xvi5uELkwK0REIuyCaoHi%2FF0s7Sw%2BM1Np%2BDqUHjcnhZI9yVFvd54Sn0o2NLURR0yKrzsqbgfq0AzvC2%2F63q9YzHxSEg7Jk7tkN9HsqD7p0YyHRme%2BY2n4MkTqf8HFZzagv%2BuQF3dXCYWil6xYH9fPotlHcP7Gcrbh7eTVZqxi8fZCtVj72wlLMEyn7Nr8Tb6sUdsmmNl%2FM6X2l4mqMLd7XqaHGfg3I%2Bqemngy3NeKvrvKwput%2Fdt9p50MZSBD0hIOyW08gdBsOsOgX4DopKL2zMFMpJa4fUDsNWQLlu5d0VNxfvNDc14%2Bc4q1r12AtL0UrmKP6cVXiaevGNMXedKV7qoFyf1KOeBvZ6yKrzsqaoY4IGqKkyZszYjeh2qiuHNmbMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmLEym65O7%2FcNb59Dlp1cnvWvuA8FoEYxnda02A2oVVr3SlbMmlyuNM3p9MYZTaf3%2B4YXZ3EZMXp7JrOdWZ36VAp%2FoyzwEUhYfkStC3XBXMGdZ%2FT3fXj%2BPr0rWbHAAuhkTt7Mrobvb5ETbA24WrRYK0al01sani9qw%2F8rU34yL2pW7vK5OPNKG7tyXq3b7%2Bges9SJXQMZSn1Kxe%2BdoOkq2488o%2B0yGtSwJqNK3aPrpWoUBU%2B19k1A4tGvBCMw4BPgpU%2FfW4n6U4nK97ewh4ZY00JeBg11evllhR6QXKfXwbudXYXvnf1kE67f%2FGQTLrClly%2BEoNR4WEUKomYndtHrT7tftKaTHYtIiiR76CUQO5VrGOd0jzfegd9tvIPFkXzy%2BgidZHthoQbeirVeo9QfhcebFqLajkWnhjUcyoum0UJyXVe3%2Bqw9qF%2B5mtHDU0G8E7uGZij4MAggIB6F2W8eVdc1xxdxfwssH%2BsfX1zXbP8CdXqdy6p1eh28%2B5Dju7K49g7Xb%2BKaPRxZaeX3zn58D6eICg8SMCusPVaM1fK19pTyhQCoSpfYqguz3S%2ByBpvejQ%2B91HpN1tBc9xh6QxTlTMP%2FscNbVfUROhd8awUqXjgitpBcV9maXA0uqO9YVGpYgTULzlNrvUYZi3VcHZQx54MgrZ6XcSeO9m2%2FEsSjL%2FEHUb%2BdlFXYlaMqq0HJvUROWteuP1%2BoGlsUI4wNy400%2Fjq9Dl4canzCFRY1nUwQykf5rYEMEnx8AKmtwsO4wkJXezZbdVFGqb%2B4A7UuMYq0JHFGyA7tObTHAodJSGcpXPeY1Q7N4J41sOofPkPDfyPHw3X2WAHcWqHpJBGfIyo8yAYZHgPfkKtzUsl2uTFUagQ%2BSri6bRgRPiqnq%2BPGI4miKK7pCsnpW0amaMRz16n1NfUc1SpqUcq8liaahugm1%2F0mUOqI47vniptMrtNbGt5RlOGqMSr81BCrhyCvmjukGp%2B0FY9YfdNJlc6wwFsFUYQ%2F3nEQqFG9Wg1I6B7z%2B%2BT33ZmV1Qfx1p5WtopFc0KSBLxD1Fo5vulKVEu2ywurogaX23R1gZ2KGXChq8u3uuoLL6lP7%2ByxHbQsLmuhEFVkiXODT0hNZx0RND0tKe8r2L%2Fo%2FZNoMsF%2FuU6vg3f3L3J8V9ZRbj23DkdJVfkBO5OYJ6oSjweEaiys1Bl28O5m8cez%2Fs8G7Zlwv2WPrKj6JBP14LrHVgxHVBxZ8XNCWh%2FET4cxcOdqOgT8mJuocvyxHY4ibqlUVVNDZ5ycGnILx3Zlp4akQezbmLEYmcKYRugSQyvVliOLW0qWuPJUZf0ndjkt1DMHCUTubajTu9R1%2FXV6Hbz7kOMTtpg%2Fzt0wu5UglG%2FL%2F%2FcJotLq4w5o1XgR8Kt1iVn10AwmkxC37qcdi7tflDU01z1mtdDAMDeH%2F2vXnFXVB%2FAwh7ddEEQ61PjmguSHHM9qsWR30C8XHiue2lCooUdVVvPkU47nPPmUXDKoHXWmu2F0tGMa1V4IelncUrLEhW1D1CvU0je0Arz%2BvCOL4wYsfPqBOr3FaRaZTq%2BDd%2Fe6KnwUXnPg3G3lfJRYPu6WktCqj1793TGBXJcYI4HB0825lAkmmKSPJad7LDLAuFWIqj6ID92OLghjMAGPNYF62COqCm%2FrZ4X2TuCj108rqalRyuyTrRCS7yCCrhCVA6IG8xHFLM7My5fFLSVLXPm00u5bU19g%2FXmKqyub%2BmL3rblfOYrrNJ3e0vAio1Wp8iuH586OYXCSfbJJrbjo6B5b800sQqqPLt5OdBHxnODHd6oFSJcE2wRqlOa8rIUH%2FKxFiQy675z6EoWeTNLNEt%2BADDBEWCipa4%2Fatae2uJQLhU5vF1Wn93uGF2dxdXoKUuged2vVp1J4JxDWdRpa4Fua8x7Z3jMnn6V63Xl5srjXkyWuPFWFjmhOW7mm6K71dHq%2Ff3gx4yBjl2P9q%2FVdRgvdr9VCqCJdAWFbSha3mKz6RNW9W2PGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzZsyYMWPGjBkzVgaDZXN7TCsYM1ZICw1dWVC6QQmPPvtzn72m%2F6DGlfrg%2FDNqWUZc2dpzuOL3PW0xqhwm1PqMVtkZlcJBHsm8P2tcK13GNnkOD%2B%2FvvpO%2BHbsxisPqZ3TdT0lXFzf2Ye9sfDEIq%2BytySDoqfXOxj4kXWUMnTfI2tidv1evSQi8FGU%2F3qbRAUwjleD%2FPh18x%2F%2B98wrtj9KtsQi0Dl3a0gpwsU01Ta0CVY1kSfqyoDYx7f3UoPtlHse8f1m9R%2FDw%2Fu67aO1PoG6H1DPn1a1SOl4QFddrXydZdXVxI%2Bzh53D1IwoQ4kq%2Fh5%2BLqB0y1nilmfHrbD7X%2F09qqq4F2cz1D9hjWZ2y6aaDrJ0hldqhK%2FBzWi%2F87eze1wtEkX3P4TKeoAZBHINZDW2ZlK4AiHASrmMPI8Y8J3i7z1NLeJafYOWmKldbLGV8kY824rdC%2F0gp47aka2qVyNlwmbtEvlUoMnF6eIeoOenV0skqdHFhmS8s6hEKDBIdWlu%2Frwkwzz797NOop9acFxXzf4yBhXhOKWbvxIP7w0Bx1aiHzdH%2BRlXVnb%2BXdxwYKLcXuGE7y4scE%2FAPPtJ8VIYXY3wC1HcHMqDG9xK1ZWlUXSrmIV9clVcFBBkPR3sKjw2n6F2BrF7Q2wWdBd2F38laNczU7bh0fJGPNs5vWUjIzsjr339h6b0Ov6zb%2Fv5PQL897auEuMQLbXleYWvkvxO6uPFF%2FC6%2BqNLFdfSL7nrgrgccXSPZpbmgaFd2%2FCjr7jrULJUd4zYeyfVBk%2BvfiUrnwo3vRmGcFuLeXAsI4oJ3qfhX1%2FSmZXg%2BdqE85%2Bs%2FfP2HttQmaV8WvnGGeusMz%2FCUyV0LZbJSX8Q3CKkRfCYgYxoqj2sV1oA0ZtTxyCxKIKtVl%2FjcGV%2FEaJP4XDEWQaSE7u7oGvmVv%2Fm1pfe6dVy3%2FS2JTFzPnF7n6n4S1FC5aHLDySp0cWEwr4NmVOriOg%2FfTVX5xTsWcdQ%2BtWV0i3W5TdnPWcPWQRE%2BhhiOgOGr%2FikuFCz5oDvJpu9DAtpiHXfbakUHKfjUV7DivsUfzw2FxkbTq0D%2BczSNomUUojZe5LVROW9JfTTIeDz7k9Uu1UI%2FopZC1cLfq%2BsjiJokkRXlSHjsBi54OSyVzGEhrlIIVOhwZxRkNbr%2FiaX3%2BnhCt%2F1lio6P%2FAKyLkw3A0ClKu%2BeChVBc2R1dHQDjwUeU%2BviVlVh4IsHUlV8lo9JCXgYR7YH34MkVK78w%2Bv98a2frJvCG%2BudFSNfnPlJRvdNwoz2X1j1QGb1b%2FfZwlGwSUTN%2Bn9Jsr5JP3z3JY6%2F96Uk23Icf%2BqPFwmlnrkZe5yfifTMRdTbTsS43Bt33pXzsnEYHXHpP9UD7eniRJ3YvX2tfQdvlS9g06OqQ1SxaQmdrPE8Uf1Se1x5WcfpxweK7xRGwZryURVKa2j7yvuc7a9eP1VzOtlFh%2F18HV3c1vxWA%2FIAFSlafEjdanNX9uHnAguRfOlIJ3981O5vkYL78j1kfIPfvGoggyPi%2BVTn%2Fw7aJZ9P4cgJVwj64SGgTiMex3fMMVtpf7xIKL3wU1a9%2Bdzmc6z6hZ%2FaWz3UyYiKgakY4zefs%2BeVMf8HyLO%2Bhf9UXUEgR9Tmj5vssv0zwJWlqkNUGNe7%2BWxSvd2VQ1Y5Uf0cXFYj3Jug8E4H3tOPavzLhzG1L%2B5zjmwAolKVz8kLJV5zMZOujm5V1WrGD6So%2BCy9eH3%2FhWaXtH9X9nxKdUvYGHf%2Bnq1wlO390OdTvbNtLPA8nII3Fg881gaP3%2F8KiIcEyLuv%2FxCdhdVbB8NSPCaUgKJw%2FQf3P7gf7wbJJ9vvLLDQmQWJ745czTsO7O%2FMBhbKNapiSCTkM8cjuBFRkzQDXOy44hn4X4HvpwcZ1z7IL6d5d%2BNPug2nckQNOakf7wSXF1lVRF3q4JgJzonD%2BqSiQHPK5ehd2cG%2FKydVYUx92%2FsMaIOacsxVsRXd3%2BcnN7o6urpzVXxrGylI%2BoBAp%2FThiPFo306%2BcR2eI3%2Fom8%2B1wTiM73mty63gWLLHz8WxI%2Fa2E3f92Qq0MSGV7Z2JxhdSJzfi52bIdePXkxu7sjCK%2Bb6%2F3XAWpCFXiLrDllcrTm3ZcLZco6qgmi2HaW9EJM8Ao%2BPyZ%2FrZoMuFJZ0l77zDkPhtyu1WgF2UzLGcmXLhdyqyylrefb%2F5eZsrE0y7Ck6%2B5G%2FndalqBdp9znh0h%2FSVk6KDKWxTn%2B90dXH1qNp4sfvS6W2gTgd5S8xVqgWgT25EYoNoZn3ra7w%2BzjYa3g%2BddcBmVO8l%2FpD4w8B7h%2FYUpiA88ZCuuAeS%2BtsObWoDvKRGzR9jwm1VvhvDr6vsCKH5Y9%2FyO7B3FYrtOJ6CQGRHuUZVQbX8Jo%2BpgiDJ5xrq0cs9bvBx1TVdaVC8iAj5fad6Duo6uWvivLaR3S28xMqTuwnOmmwqJ1Wbj3rjYXirV4W11A5G1mRaurh6VO2%2BBE5Sk3Mrkogjq%2Fn4HiB3A87AemdpOrewTUIHhMBx%2BL%2BedI36TdAN%2FGwjkKhe1idHmd%2BjjCpe2nTbe42c2NU9p3JF%2FbnqUpO6bp0OUfkkYWRKbMQwMiWfrlTail6KhNTdATzTfmenP9ZP82YqVdde88Y%2F%2FJw6rL1OooqelK4rm2%2B2W%2BBQvlXSc5J851GTu1InXedW8xotTClIDZ1Lv%2BSQng1tWcvVbrVcsb80fVmp61bTRL0LzmjJzfhS8Km66jtnogXVLan7JxCFM2HXoeZNqAxErWijfQcftDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxowZM2bMmDFjxoz9%2F2u4KsiaNO1gTOYkgWLZCarynNZV6uyy6zRcFwRkdJzX1iee%2F64%2BhRBIyIR81S6W3CtZKy%2BHR53neZrO8zLFT0NXdhn%2BH9PyuTN2Gx0sqydraWHlz8rYyAyt9KVXs7%2BJjBQLTzbfr0X0PUh2BQokTLBsuXhJvoED6LqNFxsvhph9BYoOXl3o2vjRBNN4jJlcMxzU6Azmya41r%2BcgsAakBv9R0VQdJkfnOUHUeV6O%2BLav%2Bv9p5JV9T9zzWzXescZ3caU0LHMMSkrX1kkubXlF1F7rEyWIzRaWJ1YI8UJ%2BvWSB16%2BJzg594yoW%2Fmr3rSqHCX6ZyHUDwY9U5a5rhvWhGVxmhkvQrMwqtq5ZXZvA853ZX3YnSRLZ1suo5rrhFOt%2F9umRqTbSWAaaCJdv%2F%2Bcnn2omdQbN7Mmnbv9nGAX66FQFXZ1v7QXyhNqM%2FsY5lA6rqfNcKr53VkjTlr98EMwJxT6M%2FjryNUUQRvgnSgQNv4nLHP3JnWDutsQDqSHr8kGmr5jYw%2BquIMkKxNnnZX7Ax187qszwETXn17HPiqka%2B4zguOmVi21fJv5P97%2FGGatWadrF3es8FX0iq%2BmdjbrwsGhXOdZYsTb20EsYH1DGow1HhS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2Fy8vL6%2Bvqfn5%2Ft7e339%2Ff29vbo6Ojz8%2FP6%2Bvr19fX19fWmpqbLy8v6%2Bvr4%2BPjT09Pr6%2Bv6%2Bvrr6%2Buqqqrz8%2FPt7e2ioqLPz8%2Fa2trW1taioqLr6%2Bvi4uL5%2BflVVVXNzc3%2F%2F%2F%2FW1tbj4%2BPh4eHq6ur8%2FPz%2F%2F%2F%2F29vb7%2B%2Fvz8%2FP09PTMzMz%2F%2F%2F%2F%2F%2F%2F%2F5%2Bfn19fX%2F%2F%2F%2Fy8vL9%2Ff0AAADZ2dn8%2FPz7%2B%2Fv8%2FPzp6em%2Fv7%2F7%2B%2Fvq6urp6en%2B%2Fv7%2F%2F%2F%2F4ck%2FmAAAA8nRSTlMAGgDUzwIP8SMQ759fCgUvqfDGFeIYA78fbxNTt98%2FhsV%2FBhdD4Q1rRI%2Bvwo3ATxJTD18IoKWasozTETbQ4D40IX5hC6dAMR7RXydvEsRuotKLkZCATYahkzOxQlFqmbZwJiUhFWy1wyJYcXI7gB2XIEFbgjxgiWFtfTSFMy8wSYgEqFBDTSE2KCpnSyZZUaZHRFAsDuWBYJJ7AVZQpC0Z6njBKWjdN4dlMV30iN8bV7%2BzJJeHMRiDYsR6U9yVYxdP2c1dj8CKFZZVFjtaaTxOI9cMKQk4NnBW4PKUOmiNI%2FkwWoQYUdQOSk6GvkUURFSM3n71h14AAB4tSURBVHhe7J2HfyPHmaa%2FYicCDTQCQRAkQWgABpMcDSkOw3CGM5o8Gk2QRjlZOVjBsizbcs5pndb22r7d23ybc7zbdDnnnHPO%2Bd6%2F4FjdIGu6vmp280CtbF%2B%2Fkkn%2Fnip%2BaPSDDqA%2BFOm7J3ncIoDi0NAQkY3d2IaJSws2NNZZnCouduhAsrgf7o4BYy59O4fvn3ROJQKoREkBGKqYytAJCCEQWh220I81TPFIozLaNiCMH4PJr47WIooL1C1isUUsFSwpkMqPAMARDUIFjLcYpj5tGbmqw%2BP6bhz49jZwbZ9S9k8Kd20QQLDdzFbdIz%2FJJ0OFyJFaI6mOcZ6HGOzAGxdi0tN8JL063CmJwi9FviX34m4FUrlxl0PgaBgIbrXJJfVp08yTrbq2tt99bINtCj9p%2F2TiZMMigCzYGa0WxwBgrEjxCBUici56obyLjsF%2B%2Fez8KGLwUdxVJuq9HZcpljX16lgjlaeg8hTpmUVNqubcUjzNKnBbGIBbJS6pT8nMo5ilAms3kxsAbElvsP0DqP2Ttt9KsEYIoBELpWxWDyHMocSDdUiCYMYDvJmAl5sUE%2BcDgiaiLMd6FrTJUmskFaTyEah8JPZsiru8WGL8ouLpx2rfqshkVQix%2Bz%2FOoyRIte64GalXsb5%2FJFX7J4UfxsVI3EUcMyrVrbqAtbVVB1x96q39f4Yo0goYpBJ6EmhWa31nx3WrUmskFaTyJah8iVSofNrqY2umHOeNsyIQ457ksUTnlP0dq4NfVyuLrpTKLlHy0sUp1UASq%2F2Txr2ASAiiwJvNYrVzBLjUbJ4BjlS0qbdE%2F%2FStUgAExAMyWG2jI2EFDd3qujNsWcPOesxquY6d1OOSmiMbId4YCTT%2BBEq0xDjRKACM8mO1HwF2mYm%2BDnRdrRRht5hUmRPHAeD4CdL3jwBEBQ3OheC84VE%2FXi2L1Q9fB14kOgFc%2F%2BzeVgmgJKuVTnzsPSh2iFoncY82uVrw14aH1%2FxCNVbszO4heYa0vDPk30uc%2F%2BOxv2LgBAAGdjSM8R548OvqoxHiUl0bYWyX7R8h1P5J22%2BHUIlAxXSl5FYDeZS67hHgTO%2F%2F2aoPbWy12r9JqFVifFsqsLYGbGtlJyq%2BV2TuBRrA3WTgs%2FAY70S30519XFebg19X3520%2BbakctBO2j%2BZ%2BNt23qsdwduyWCWnjjB1h%2FZvdWkqhPxKVhi3gMamh2Ilhn304xeIaTVJpVlsTp9FLRt3F9DPgvtmX1czbf4FSeXghcT9k4WXLYxtg8oYrLJRKZNTC7XWa7R%2Fq1RDCDfq7RltpDwixPTcjIdii1R87MYnptUktdKYn6Pz89ZSJj6l6k8NcA%2Bc9bqavvmF6jbdHqwW0vYP5%2Fq9dLGo7qVTrY5OXKnXr0yM7m3V%2BFzIAs4S0crEckCmBDOedY1UCmI3%2BtN0LjUucan0yDOycjD8PZk4VJDCB3%2B%2FqmmtSqlc68g2dUYKlLJ%2FUrgzMl73Gu3xESfFqorzwO0OsXiI4kmrCe%2FSRoQ4T3slOK2ea0qa001Tgci0E2TiQkVk5tHooO9XnYJDWcP3TzovT4xOL5dJixDqXz29gHhGRZTRIRogzT2l5mk6b8F%2BG5KhtyB5%2Fj%2B2mie3mie3mlvNk1vNk1vNk1vNk1vNrZbouy65VR8%2BsST3UJbGpopjJYZdoNsFXGOptDrpfAn9LGWvU5xaLJFvmr9Ycu3kzstYuiHrUuaUFsfGFg%2FyQOFa%2BHaCIAeHMNTnPgA%2FwSrnrg3UPPD%2B1R8AHnwQ%2BIEUq7xONv4w%2Brk7ex2vBhRhng9ks%2BoyGAXU6XYrROTzXnTg4PrRW3EAIQQI8tueVn3I%2BGarnNuoz4%2BOztdZ%2F%2Bpl4KWXgMspVnmdbHwWIgxm91XHA7JxiJ1A64jHvJg0WS0CmBqzWf3NLSG2NmGTnopCOm8l8RZKpNsDSbG0l1UfUXyjVcZLqE8EoGCirj1cC%2F20Eq3yOgjrML6wwHgLFoWxUGHzicx1iB4CQJy7Iee7S4biAw4QUM9k1XhodzE%2B1yRqzo2zk3YXkPZaZODoEJl48avVU5pVQQjFJltVUgHfZJX9N%2FDDuJ3Cerdr%2FasvA5icBPByolVeB6yO5B2go%2FOXdzpJLuAVVseuGOv0%2F2M%2Bce6EnO0uIRO3elPbciars9UyhSlXZ%2FkJvoVSCS3OaeNRCTi%2F59j7UGFc0J7XVSWVad2hpv5VEO9fPQXgwx8GcMr4CRybTHWg6ijungJOuRo%2Fhp%2BgMD%2BBw4Y6Xb3OrOSG1BTPdKxCJZNVfJn6%2BbKhTnMcGG9yTv%2B5Zrb6CQT4LLtQEAkBIRKtFgR2IgpZrDa8aEzvX60AQBAAQIVi6bdzEa9jA7aso3FnGph2NA58ncJ8HTBsz5%2FQ69QkD1OM9TmNju7yYsqxmtFqI46fo36eg8HSzwM%2Fb7L3fR6RkYPwfTdzQVBtOklWuT1ulfevCiH0%2FtV7sZt7zd1ovM5F4KKqozgBpHMA6BB1AIDNb0yuGOvIVPAk8YT1BztW3fq5rXMb9fZjcexEEwEHpjPw%2BLjxDPwH2xHgvIIPMy5EBqtCiBSr6f2rswAaQjQAzCbsFVYn2NwMVB3FCWD1AeC9RO8FADb%2FmZ6az7fzcf15%2BWr7BzhWnYnV5irr1gPtWCX9swSbQHOrXN5qck61ByTgfPY9DzUC%2Fs6GICfsbVXCFKtp%2FatL%2FY9pHQKAJUOZyUnwOnNzYR3GhWAcKmDzHbU9GfpsvfcpPsh11ZhNZXVTG5qbt6hJ8l%2FOT%2FeITPyjX6l9kG8mqe0cwGp6%2F%2BrdAHCd6Lr%2BewKopNbh3Gx1kDoET%2FHBrqvGzCmrc6QlGFFA480k3jxdZpsJEoCgeE8lhfdQQ2JocjKj1fT%2B1RoAvJ%2Fo%2FQBQS7fK63CeZjW9TsOrM14dHW%2Br%2Ban6vF3qZbJKyurBpGnQQpicNDY0E4aAXnQC73%2BNh3XZsv5V1ow6RzQnv4%2FyMjJZ6nDO64jMdaZHJxgvUHnZND%2Bh%2FuguHdXmU0KEUF8PPpES0esZG5pJDAkxdDPOk%2FdC5Mmt5smt5smt5smt5lbz5Fbz5Fbz5Fbz5FZzq%2BYGw13usyHXNjcHKKrHZwuvpKWLinmDsECGlAwdND5R2vIg39VWq0atfV5Y14fs2ryIktVqjbUepmUW9zI2CUyes9AlnvJZtEfiaAEL%2B7OabBqJQ619rSnT4jwKiCHaRaD08MdFvVDnWhVXWpm9jFYrEf5AwoYQz1INNQZ7QG91GJfJkH%2BGBzSyghWyJoUAhJi0SIXRAaw292W1eSBWE4uI3YAIGAOYVsWl1sGsvhLhY3FahN6SqXLs0xZKxud5QurmeQee0xGIRnrRD%2FVGFE6iJKIQj0gdYsjI1RCzKhErnWrVj3Hy0Y3OwCDaqx2Ya92%2FVeBYhK8DbLplAbcC7MT2vh%2FEMZPVyhraZAjgMGRe9S2RQiWJg519D%2BoMnPi4e1n1oReZJXLHKtJqNUFrNaZ1EKuzIswstzp%2B6dK44Vm%2B3Ah%2BCmiZ9%2FsDxFNBnX6%2FrTYVHuwMvJBmdcFs1YdmtYp7yLVRdEFUSNBaiGsdwKqKxq0vAF%2BwuNVTn%2B68buH7uQqxdRYnXWL5XXxtYKtChfHEgcHPwKEeSixPJO3BZHVdt1oQc64NwEZM3zqpxPn6%2Bpth9fiLwIvHmdUOwswaVDTPb%2BB%2BYnkYP3dwx2rmu6XWQZyBhdgogHj5XYTChhCm%2BoWqZtXttn4EYW7Wpy%2Beqbi%2FXshk1dqy9mMVH9ja%2BgCY1YcsIcQW0DGp%2BGkcJpYbeGlfVktAaXCrzYM5A6%2FQ3lZpJWE7C9UYr0wBP4kwSh%2BTKrmSmsWqNdwctrhV0Q%2B3ipMnway6eF7usjYe4lZbpRpeIBbge%2FZlVZnI0nyXOjD4PTCHu8hk26tvh6gQ5ypKH5MacSWVW63G9VnDTriYLnNRhEyLdWSaWzLX8AU5%2Fkn98zpXwW6X1Mj%2F0NkCFhKOym0emVgYbKXag74HNtchGGyPTmyH2VbZ1adLVbykpGpW41xKJalV34qd30KwjkxjS2YX4WLXFfY%2BFmEakz3SYpt%2BH7lSXWFHJVud%2BvfXanNAqzxpj1vQpSpeLmQ7VUmpUivrTw9EmDJlyty25SD6oVHD404zqTQiMaOF3R%2FS%2BIboZ6Mw4PrDB3UGFpRchxTkSX3cwePQd0ZW2P8ZNHkvRJ7cap7cap7cam41T241T241T241T241t%2Bq2aOAs0rdVcquuXawYFrpdTF6%2Fl6eDJUqOu0SDxvdpH8mtus8eR9HUnQ3ftK4vANslPSdxisOlKcjZ8uc6jI9Ryzy%2FWKEuq%2BUn9KOHW5VA%2BVASn%2BrQAcR2wy%2FJvAWwoYjyuD4vFDnwTdi33ZhV1z55ybJYx0B9sw2UDOvrRqK0dAHcZ16C2xp2T1ywntO4d3aCcJXPH696M4EPm0s1aQWkISRQPpTEgcUWGQKAkLknBtIRlFbGm6yUokyeHDJyGLT6QKRVTcPJS8P6Wq%2F1ibnlNg4b1tcFwHR3jOunn8KmEGLkhG3fMeJofPR8yQcWXX1%2BuTAa%2BMAFTWpBAKLAtALSEBIoH0riAIrdwa1KEVA2OAfMQyZ5csjM14llHX2tahqOX2PLSr0%2F6kkwrK9r6ts%2BFcKaq1eZix7h%2BAnG%2B4uZr%2Bl8oUK%2B3p3hLiJURVhkjyANgQzUOJTEIWN3BrUqRSgbBs5KKcrlySHOE1tXIq1qGl8V1MPh0KJlWF%2FX0AVYQjuk9xuvb7CGTzB%2BP6w6UL1D4wsoLrLttrEbW7cRjpGR8iFXcaMl3x3UKmxlw8BZKUWZPF6IS%2BVauVSVNjDWHQMu8PWBI6u1%2BEFc%2FaTBNQE7Um3Gf3RrZMIbLzgaf6cHKTV%2Bgr%2BgrF4w2iAj5UNrGmeWpga2GmXNzHkpjbKXsc22v5HUutIAsDbEpao8gCg%2FxtcHJsn19XV%2F7kGE4VafkvVtMF5oEp0ul3QezHhSKvTXYfSpJ%2FY6BSylSKd86A7FjZaqzwxsNXqEOxI4K2WmI2InI3z7fTLGDx93KHxLY5ZKvQ3IbDYN6wMDgLa%2Brnf5i16C1Y%2BMb9cHGJdp%2BpwHMxsFAkjTGg3qUgkYlo7MlA85ihssWZMFZ1Cr1rA6TgycWzVTFcP2%2B4lSh50hoqfkWxopleddFoD6nGl9YAD6%2BrptrB2SuE6xNNClubLjdtFgfDtmHqworrRG72x0qQSEokzUOJTEw7daI71B75akTyXVwFkpTrlVrjVZ6hDRZZy8ZJZKzkUPjTNkWh%2FYsJL%2BxzzIeLfH8Z3YyZ0D8eS2ZSAUlUD5UBIH2qfPD%2F7ORvpUUg2clTJTocK33%2FzOpi91iFqwfvCaQ%2BYEM43H1FjKerzN01UPqJ4O4nj1XAMyjXOrA%2FHktmUgFJVE%2BZBELueNyeVmQk8mZW7dJ2nI5VIljwaZP0Z5uFZzU34kdYiubY2cdygpwbRylLoeb7MwKkSB7ZjVaSEzvToYT25bFkK1IXPKh0LkcD7dowNIVNkx8ugLO%2FY4TddqbsqPpA6R06TvvORxEnDeCzFo8l6IPLnVPLnVPLnV3Gqe3Gqe3Gqe3Gqe3Gpu1dzf%2B5Zx1ShxcPUHT2uqktR9uN%2F4ST9UWThIq65taI95S7gaAsyddTWPzc%2FCB85JnHT3ZdVuUULel2C1UsTCYK8at0XAUMsNrdqm9pi9uQd4%2B5kPq569Prk%2BgOISkaEPeXS%2BDns%2FfJzXJ2oplMnGAoC1fVlV28%2FkGVX529x750BW5YcvgEox7EYrAYAQrL835ICJW09Xq09b5vkNGPi5kYl5jbPHVVmrjQMfqpWI9SE%2FQvTIRB0lnQdEgZlXarw%2BLRVBaTZ4o3opu9XOVQALCVK9%2BaqxkjcTDGT12RqKQBG1Z4eIDgMAEevvlVyGc2%2FYKRScYc8033pmHIxbq1crgZWxPrm4qwyc%2F1CN9D7kCnwfldtxTOPRRxc4j3biuOLqyKOEmGy0apCptTJa7RYRxnTc3yvlFYxWpdRBrDZnPIQvjuYQUQ0QgkgIredTchnOo5PRGufWZH3Y%2BVmPceDUZ12Ac1ld5zt%2FBF1G60MOqkA1CLxZjdPVlo01zkOpM%2BU4b9kpa5oxGyf7%2FGQ2qz5UCyrLyoaSp1V6KKVtKfvirkNEDWCH1khlL74u8Trnl3oTTqXIOXBnbw0mTgSdQ6bXg4zeh7wePrZX0%2FjVsF%2BS8UhqoPEppFhlNkaEAKA3cJJtvi3oYCfWY4a73BUu1Q%2Bri8JBWj0UjbP%2BXsllOPfCRtc7PJ3L%2B8RKMXsd8%2BOKKzgngMmqJ4TWh1xBtSq%2FHtL4j1uyC4vxUiRV449ZKVa5DfNBecmDjHcpjh9FYyM81VSHg5S7XHZXPJBVMe9J2JgXQ0Rvi8ZZf2%2FIARO3Xd93bc5hd4rmOkIYuSASOienWisBf7J2F%2Bl9yMF8oTAfHNHrHHGGq8MOMY5Qqs6D4SqApHUDlY1Uq803IPNGM46xOb3S60F9JIHd5Wa7K%2B5vjcj8B%2Bdbxei9SbE1FPb3yrD%2B3r14ESgmzR%2BUE93xaQC1u8q8D1neA4%2FxOmO%2FUHAqBo67AmKcnMK4B0qIspFqlVY3AGysanRzTgJrppx2l8vvige7W7pmeTPAjGddG%2Br394L19751nJzCFeDpsrEPucjmZ%2BdK%2BIxFhjAbKVZpxYK1osO56MGDlLtcdlc8sFVn%2BHQABKdl735Cf%2B9bwtUQwOBB1g%2BGiYfZSLVKFxuXyBwn5S6X3RUPbpWcJgkx1JS9%2Bwn9vW8lZ82xB1%2BfiU4ZEOYNCqablDXqLlfXGuz1M3kvRJ7vZKt5cqu51Ty51Ty51Ty51Ty51Ty51dxqntyqe5W%2BrZP3A3dhd4g6NrpkSqc7BibV%2FgjtM4twDXRsjIyxYXMI9dUcn7Lk1VdfVd%2FexFSAA18nOXs%2F8GGrhoUF1KzDxOyVbAAvMKv34RNkSGdxbGyxY%2Bb%2F%2Bs84xFKCefnoFoCUngEebT3LoppfjM265ZZb1Lc3Ma94IgbcItsUxlPWSWZWk%2Fty8fyMBXgzzzN5lSkAaH%2BNDdTwx2jM1aC7iDCLrpE%2F0XLZ86kBNZd4mvuwiv5f%2FAwt2sb5yGrV9d3kA8b3GfUN9Yus0YdvTzrn6ySbrZYAWEJYAEqs6tGjkDG8iBrjj8Mj1oh1N71g8xZ6dTLg%2FHvvk1w75Ot13JexOUCoMNvFViQVFzJYnZubU9%2F44svmAyb6ptNCFWHM%2FVvvT9p%2BkdFqtE4y36DIqi%2BtHo6a%2FGp6X64AgNtuAwBBsawB3tnpf6e%2F6Ih%2BE8DCC9p1%2BAjaaABAFUdM%2FE%2F9Zcm1C8%2FHPw5UiMUF4GY8VoWY96zXZfuIQLWQwSoA9S198WX3BqRAH8AN7TBadAv8L36%2Fhp28lO1YbTDbKuaO1cgq%2FKFIJ1yXrwGrrLLzrHX661PsRbfUbQKsTBfWu%2FHRNoAfs9Dl%2FI87KxZ7HWwCm8o1270Zr6vB6T8ddRkqqZmtmhdf5qsJTmktOoVJQCw7hl3%2F09jJV7JZ%2FWAJKsUUq%2FrfgG4AwFNP8fV%2Bj27nttvkV%2F1Qsi4egcwXY%2FzyjxKssFqLVB7Edae%2B9gBQb17Hgzfz49v8d%2FAXiUKuUkLjV4FfbaBkasYDipUYhdj9h7T8QhHe2%2F820TrtzyqX2kjSyhYX7QHmXf%2Bz6KfRzGS1UT4FlXtSra6ryevJ%2Fbp0224ols96zxchU9c3bwrX7wSA10llro7umXcA9TNd1Odi3Jf8E%2BTHOLk1fMZpt53PoObqUtsA2kpryrFakVJPFivqHjijVSa1Ol2VWolpZVKJkqwGHqI8SZmsfrADFXzRZJWvnyyDaoH166afgXuHEMY7wzfvhVUA6N2Mz1i4f0KIiadgndH4kY9b6HU1fh%2FaPXr8ceq1tcWwi965ZQDL57xilmM1%2BszJb9b023sPO9Hu9uqA36n4QDum7gLkbipUgQvEtTKpBCTcqI6KMN4ns1ktPwqVapNb5Vqj62q1wPqB0626dv%2Fm52mHLeiOBypyRHvqbUwtLEyhPezEeRXAn22hGuMdeB%2BLtvpjHjqx%2BqdXZfXK6ul20rHK%2B2%2FDjxTFhIwKwLoiZEbJ2Nb%2BOFvnVH3TtUYbzy35ScveVvCJbFZbUMGXs7yzKURWC0OsHzjdqn18a1rMzwvWDP2xBsZ7D7GVyclZnnzyHe94cnLZ0Xhh8vfwR1%2FU1s4%2BiSj880rLTYrelzeXsxyr0lpAFIyyNd1hXuS6XEeYepmvc6q%2B6c%2BBVYLSKqVyTc9ls3ofVKxeyjrJrBeC9c2mWD0%2B3CQKAmJpPrNVJlisDlFveWJiuUfE%2BGv4B804ryCWCsXSmBfzjf3%2Fbiku1Y2k8pzZ8ABv4wwNFBGlwF4HTYFtDuFks1qDyvNp6yRzq6pvlm%2Fe6ip7uzTs7NFlTGKkTNmzIgKNBCIWbXg6oGA6bclrngJbG9gYZ2VUiNEVh96sCCmdwYQnMCpUmJtC4YB7IRz67kneC5Ent5ont5ont5ont5pbzZNbzZNbzZNbzZNbXZhaiIPcagtRii5ljQsYJy%2B4rnn3dlGkNzH4KFomHIbz0liR9T8fKF%2BcmlqUnMcdA7qUKXt0xNqAbZgeWu3%2FwFfRz4%2BQKa2rLUOTAYoV0%2FK0tg1qceFu7SzMi58i4Ul2i6a9VUzYIWiimdnqm7%2Fu8amv3XPna5LzHEFjck6C9P7kvZrRhICBhVZFNPYw%2BnmYWNzSGH7lGjR6yrhW47OwJbfxLOm53%2FspZhX4w8AFcXTDcJh1pn7jDRAL3viNqY7RK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<h1 class="title">Quiz 2</h1>
<h4 class="author"><em>Liam Damewood</em></h4>
<h4 class="date"><em>September 7, 2014</em></h4>
</div>
<div id="question-1" class="section level3">
<h3>Question 1</h3>
<p>Consider the following data with x as the predictor and y as as the outcome.</p>
<pre class="r"><code>x <- c(0.61, 0.93, 0.83, 0.35, 0.54, 0.16, 0.91, 0.62, 0.62)
y <- c(0.67, 0.84, 0.6, 0.18, 0.85, 0.47, 1.1, 0.65, 0.36)</code></pre>
<p>Give a P-value for the two sided hypothesis test of whether <span class="math">\(\beta_1\)</span> from a linear regression model is 0 or not.</p>
<ul>
<li>0.05296</li>
<li>2.325</li>
<li>0.025</li>
<li>0.391</li>
</ul>
<pre class="r"><code>n = length(x)
beta1 <- cor(y, x) * sd(y) / sd(x)
beta0 <- mean(y) - beta1 * mean(x)
e <- y - beta0 - beta1 * x
sigma <- sqrt(sum(e*e)/(length(e)-2))
ssx <- sum((x - mean(x))^2)
seBeta0 <- (1/n + mean(x)^2 / ssx) ^ 0.5 * sigma
seBeta1 <- sigma / sqrt(ssx)
tBeta0 <- beta0 / seBeta0
tBeta1 <- beta1 / seBeta1
pBeta0 <- 2 * pt(abs(tBeta0), df = n - 2, lower.tail = FALSE)
pBeta1 <- 2 * pt(abs(tBeta1), df = n - 2, lower.tail = FALSE)
pBeta1</code></pre>
<pre><code>## [1] 0.05296</code></pre>
<pre class="r"><code># Easy way
summary(lm(y ~ x))$coefficients[2,4]</code></pre>
<pre><code>## [1] 0.05296</code></pre>
</div>
<div id="question-2" class="section level3">
<h3>Question 2</h3>
<p>Consider the previous problem, give the estimate of the residual standard deviation.</p>
<ul>
<li>0.3552</li>
<li>0.223</li>
<li>0.4358</li>
<li>0.05296</li>
</ul>
<pre class="r"><code>fit <- lm(y ~ x)
e <- resid(fit)
plot(y ~ x)
abline(fit)</code></pre>
<p><img 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gQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQILERglYUsZBkCixC4V5Z9frJsEX1YlAABAgQIECBAgAABAgQIECAwKwLXZEdfm9wwKzs87P1cfdgd6o/ASgSq+Hn0SubxNgECBAgQIECAAAECBAgQIECAwK8Fzsno+3/90tggAgqgg2iZdxgCzZmfH0lnJw+jQ30QIECAAAECBAgQIECAAAECBKZU4NDs115JU0+Z0t0c7W4pgI7WV+/LF6ji5xuX/7Z3CBAgQIAAAQIECBAgQIAAAQIzL1DFz4q2CIFVF7GsRQkQIECAAAECBAgQIECAAAECBAgQIDDRAgqgE314bBwBAgQIECBAgAABAgQIECBAgAABAosRUABdjJ5lCRAgQIAAAQIECBAgQIAAAQIECBCYaAEF0Ik+PDaOAAECBAgQIECAAAECBAgQIECAAIHFCCiALkbPsgQIECBAgAABAgQIECBAgAABAgQITLSAAuhEHx4bR4AAAQIECBAgQIAAAQIECBAgQIDAYgQUQBejZ1kCBAgQIECAAAECBAgQIECAAAECBCZaQAF0og+PjSNAgAABAgQIECBAgAABAgQIECBAYDECCqCL0bMsAQIECBAgQIAAAQIECBAgQIAAAQITLaAAOtGHx8YRIECAAAECBAgQIECAAAECBAgQILAYAQXQxehZlgABAgQIECBAgAABAgQIECBAgACBiRZYfaK3zsYRIECAAAECBAgQIECAAAECBAjMikCdqLdzsnVyY3JBckmiEViUgDNAF8VnYQIECBAgQIAAAQIECBAgQIAAgUUKbJnl35RclPwg+WLyjeTi5PTkaYkaVhC0hQn44VmYm6UIECBAgAABAgQIECBAgAABAgQWL/C4dHFu8sJki+SC5KTk1OS6ZK/kX5OTk3pfIzCwgALowGQWIECAAAECBAgQIECAAAECBAgQGILAk9LHR5INko8nuyfbJ49M9kk2Tw5NfpY8NPlKsnGiERhIQAF0IC4zEyBAgAABAgQIECBAgAABAgQIDEFg2/RxfFK1qVckj0++m7TbLXnxb0mdBfqdZJfkXYlGYCABBdCBuMxMgAABAgQIECBAgAABAgQIECAwBIG/TR/rJu9PXrmS/i7L+1UgvTZ5YrJ/ohHoW0ABtG8qMxIgQIAAAQIECBAgQIAAAQIECAxBYO30cVDyi+QlffZ3YeZ7c2/eeiiSRqBvAQXQvqnMSIAAAQIECBAgQIAAAQIECBAgMASBvdPHOkk94f0nA/R3Ym/e3xlgGbMS+OV9FjAQIECAAAECBAgQIECAAAECBAgQWCqBe/ZW9N8DrrCZ/x4DLmf2GRdwBuiM/wDYfQIECBAgQIAAAQIECBAgQIDAEgvc1lvf6gOut5n/9gGXM/uMCyiAzvgPgN0nQIAAAQIECBAgQIAAAQIECCyxQHPZ+24DrreZv1l+wMXNPqsCCqCzeuTtNwECBAgQIECAAAECBAgQIEBgPAJ1788rkvsmew6wCYf25v3sAMuYlYB7gPoZIECAAAECBAgQIECAAAECBAgQWFKBO7K2d/XW+KYMm0vbV7QRVSg9PGkvu6L5vUfgVwLOAP0VhRECBAgQIECAAAECBAgQIECAAIElEnh11vPz5KHJCcmayfLa7nnj48my5K3JDxKNQN8CCqB9U5mRAAECBAgQIECAAAECBAgQIEBgSAJXp58nJNclBydnJockGyRNu3dGXpOckmydfCE5OtEIDCTQzynGA3VoZgIECBAgQIAAAQIECBAgQIAAAQJ9CNS9QPdNTkzuk7w3+UVyZbJ2sk5SraYdm7wwaZ4gn1GNQH8CzgDtz8lcBAgQIECAAAECBAgQIECAAAECwxc4O13W092fmZyUVIFz06SKn5ckxyUPSo5Mbk00AgMLOAN0YDILECBAgAABAgQIECBAgAABAgQIDFHg9vRVD0WqrJJsktyU3JhoBBYtoAC6aEIdECBAgAABAgQIECBAgAABAgQIDEmgLne/Ykh96YbALwVcAu8HgQABAgQIECBAgAABAgQIECBAgACBqRVQAJ3aQ2vHCBAgQIAAAQIECBAgQIAAAQIECBBQAPUzQIAAAQIECBAgQIAAAQIECBAgQIDA1AoogE7tobVjBAgQIECAAAECBAgQIECAAAECBAgogPoZIECAAAECBAgQIECAAAECBAgQIEBgagUUQKf20NoxAgQIECBAgAABAgQIECBAgAABAgQUQP0MECBAgAABAgQIECBAgAABAgQIECAwtQIKoFN7aO0YAQIECBAgQIAAAQIECBAgQIAAAQIKoH4GCBAgQIAAAQIECBAgQIAAAQIECBCYWgEF0Kk9tHaMAAECBAgQIECAAAECBAgQIECAAAEFUD8DBAgQIECAAAECBAgQIECAAAECBAhMrYAC6NQeWjtGgAABAgQIECBAgAABAgQIECBAgIACqJ8BAgQIECBAgAABAgQIECBAgAABAgSmVkABdGoPrR0jQIAAAQIECBAgQIAAAQIECBAgQEAB1M8AAQIECBAgQIAAAQIECBAgQIAAAQJTK6AAOrWH1o4RIECAAAECBAgQIECAAAECBAgQIKAA6meAAAECBAgQIECAAAECBAgQIECAAIGpFVAAndpDa8cIECBAgAABAgQIECBAgAABAgQIEFAA9TNAgAABAgQIECBAgAABAgQIECBAgMDUCiiATu2htWMECBAgQIAAAQIECBAgQIAAAQIECCiA+hkgQIAAAQIECBAgQIAAAQIECBAgQGBqBRRAp/bQ2jECBAgQIECAAAECBAgQIECAAAECBBRA/QwQIECAAAECBAgQIECAAAECBAgQIDC1AgqgU3to7RgBAgQIECBAgAABAgQIECBAgAABAgqgfgYIECBAgAABAgQIECBAgAABAgQIEJhaAQXQqT20dowAAQIECBAgQIAAAQIECBAgQIAAAQVQPwMECBAgQIAAAQIECBAgQIAAAQIECEytgALo1B5aO0aAAAECBAgQIECAAAECBAgQIECAgAKonwECBAgQIECAAAECBAgQIECAAAECBKZWQAF0ag+tHSNAgAABAgQIECBAgAABAgQIECBAYHUEYxfYOluwSbJOLzdneE1ybXJFUq81AgQIECBAgAABAgQIECBAgAABAgQWIKAAugC0RS6yfpZ/WnJIsmtSr5fXbs8bZyWnJp9IPpX8ItEIECBAgAABAgQIECBAgAABAgQIEOhDwCXwfSANaZYt088xyc+Ttyb7Jisqfubtu1WB+oHJkUkVQL+bPDbRCBAgQIAAAQIECBAgQIAAAQIECBDoQ8AZoH0gDWGWjdPH55PdWn3VmZwXJT9NLktuSm5J6pislWyQbJNsm6yZVKszRj+WHJW8MdEIECBAgAABAgQIECBAgAABAgQIEFiBgALoCnCG9Na66eeTSVP8/GbG35B8IanC58rassywd1KXzR+W1Ot/Ts5N6pJ4jQABAgQIECBAgAABAgQIECBAgAABAmMTqKJlne1ZeV+ymNsOPCbL39rrqy6HX0xfWXwsrYq3ZfHisazdSgkQIECAAAECBAgQIECAAAEC3RE4IZtadZRDu7PJk7elXSygTZ7iirdov97bVbCsszjvXPHsK3y3zvj8894cdUbp9iuc25sECBAgQIAAAQIECBAgQIAAAQIEZlxAAXT0PwD791bx8QxvG8LqPtTqY5fWuFECBAgQIECAAAECBAgQIECAAAECBOYIKIDOARnBy3v2+vzZkPq+Iv00hdS1h9SnbggQIECAAAECBAgQIECAAAECBAhMpYAC6OgP63m9Vew7pFXVJfX1IKRq37lr4L8ECBAgQIAAAQIECBAgQIAAAQIECMwnoAA6n8pwp32r190fZ/jwRXa9UZZ/fa+PKzM8f5H9WZwAAQIECBAgQIAAAQIECBAgQIDAVAsogI7+8L46q6hL1tdKPpockayRDNr2yAKfS2pY7e13DfyXAAECBAgQIECAAAECBAgQIECAAIHlCay+vDdMH5pAXQL/suS1yYZJFS5r/OTkjKTO4rwkuSm5OaljUsXSDZJtkp2ShyW7Jk2rQuhfNS8MCRAgQIAAAQIECBAgQIAAAQIECBCYX0ABdH6XYU99XTqshxcdk9SDi9ZP/lcvGQzUPpO5D0nuHGgpMxMgQIAAAQIECBAgQIAAAQIECBCYQQGXwC/dQT8uq9o2+Yfk4gFXe0vmr8vnH5c8Oqn7f2oECBAgQIAAAQIECBAgQIAAAQIECKxEwBmgKwEa8tuXpb+X97JdhvskOyd1uXtdHl9nhtb9Qq9Prk3q8vnvJ2cmNU0jQIAAAQIECBAgQIAAAQIECBAgQGAAAQXQAbCGPOsF6a+iESBAgAABAgQIECBAgAABAgQIECAwIgGXwI8IVrcECBAgQIAAAQIECBAgQIAAAQIECIxfQAF0/MfAFhAgQIAAAQIECBAgQIAAAQIECBAgMCIBl8CPCHZE3S5Lv1u2+r6wNT7q0Vr3KkNYiaL7EBB1QYAAAQIECBAgQIAAAQIECBAgQGAaBfbKTv2ilaXax9e31tle/2LG/3OpNt56CBAgQIAAAQIECBAgQIAAAQIdFTgh2131l0M7uv0TsdnOAJ2IwzDxG3FjtvDmZBhnb9bPXPWzSaIRIECAAAECBAgQIECAAAECBAgQGKnAMApaI91AnU+EwF9lK9ZO1hxCzujt0RW9oQEBAgQIECBAgAABAgQIECBAgACBkQk4A3RktCPp+Mz0utVIetYpAQIECBAgQIAAAQIECBAgQIAAgSkUUADt1kG9PZt7Sbc22dYSIECAAAECBAgQIECAAAECBAgQGJ+AS+DHZ2/NBAgQIECAAAECBAgQIECAAAECBAiMWEABdMTAuidAgAABAgQIECBAgAABAgQIECBAYHwCCqDjs7dmAgQIECBAgAABAgQIECBAgAABAgRGLKAAOmJg3RMgQIAAAQIECBAgQIAAAQIECBAgMD4BBdDx2VszAQIECBAgQIAAAQIECBAgQIAAAQIjFlAAHTGw7gkQIECAAAECBAgQIECAAAECBAgQGJ+AAuj47K2ZAAECBAgQIECAAAECBAgQIECAAIERC6w+4v51f7e7XRaEVUYEsdmI+tUtAQIECBAgQIAAAQIECBAgQIAAgakQUAAd/WHcJKtwpu3ona2BAAECBAgQIECAAAECBAgQIECAwG8JKID+FsnQJxyQHo9Ldmn1fHHG72i9NkqAAAECBAgQIECAAAECBAgQIECAwAgEFEBHgDqny6/n9T7JZ5K9e++9O8OX98YNCBAgQIAAAQIECBAgQIAAAQIECBAYkYBLs0cEO6fbq/L695JzetNfmuEje+MGBAgQIECAAAECBAgQIECAAAECBAiMSEABdESw83R7baYdntyZlPsJyQaJRoAAAQIECBAgQIAAAQIECBAgQIDAiAQUQEcEu5xuT8n0t/Te2zrD5y9nPpMJECBAgAABAgQIECBAgAABAgQIEBiCgALoEBAH7KLu/Xl+b5n/k+F6Ay5vdgIECBAgQIAAAQIECBAgQIAAAQIE+hTwEKQ+oYY42w3p6ynJ43p9bp/hWb1xAwIECBAgQIAAAQIECBAgQIAAAQIEhiigADpEzAG6OjXzVjQCBAgQIECAAAECBAgQIECAAAECBEYo4BL4EeLqmgABAgQIECBAgAABAgQIECBAgACB8QoogI7X39oJECBAgAABAgQIECBAgAABAgQIEBihgALoCHF1TYAAAQIECBAgQIAAAQIECBAgQIDAeAUUQMfrb+0ECBAgQIAAAQIECBAgQIAAAQIECIxQQAF0hLi6JkCAAAECBAgQIECAAAECBAgQIEBgvAIKoOP1t3YCBAgQIECAAAECBAgQIECAAAECBEYooAA6QlxdEyBAgAABAgQIECBAgAABAgQIECAwXgEF0PH6WzsBAgQIECBAgAABAgQIECBAgAABAiMUUAAdIa6uCRAgQIAAAQIECBAgQIAAAQIECBAYr4AC6Hj9rZ0AAQIECBAgQIAAAQIECBAgQIAAgREKKICOEFfXBAgQIECAAAECBAgQIECAAAECBAiMV0ABdLz+1k6AAAECBAgQIECAAAECBAgQIECAwAgFFEBHiKtrAgQIECBAgAABAgQIECBAgAABAgTGK6AAOl5/aydAgAABAgQIECBAgAABAgQIECBAYIQCCqAjxNU1AQIECBAgQIAAAQIECBAgQIAAAQLjFVAAHa+/tRMgQIAAAQIECBAgQIAAAQIECBAgMEIBBdAR4uqaAAECBAgQIECAAAECBAgQIECAAIHxCiiAjtff2gkQIECAAAECBAgQIECAAAECBAgQGKGAAugIcXVNgAABAgQIECBAgAABAgQIECBAgMB4BRRAx+tv7QQIECBAgAABAgQIECBAgAABAgQIjFBAAXSEuLomQIAAAQIECBAgQIAAAQIECBAgQGC8Agqg4/W3dgIECBAgQIAAAQIECBAgQIAAAQIERiigADpCXF0TIECAAAECBAgQIECAAAECBAgQIDBeAQXQ8fpbOwECBAgQIECAAAECBAgQIECAAAECIxRQAB0hrq4JECBAgAABAgQIECBAgAABAgQIEBivgALoeP2tnQABAgQIECBAgAABAgQIECBAgACBEQoogI4QV9cECBAgQIAAAQIECBAgQIAAAQIECIxXQAF0vP7WToAAAQIECBAgQIAAAQIECBAgQIDACAUUQEeIq2sCBAgQIECAAAECBAgQIECAAAECBMYroAA6Xn9rJ0CAAAECBAgQIECAAAECBAgQIEBghAIKoCPE1TUBAgQIECBAgAABAgQIECBAgAABAuMVUAAdr7+1EyBAgAABAgQIECBAgAABAgQIECAwQgEF0BHi6poAAQIECBAgQIAAAQIECBAgQIAAgfEKKICO19/aCRAgQIAAAQIECBAgQIAAAQIECBAYoYAC6AhxdU2AAAECBAgQIECAAAECBAgQIECAwHgFFEDH62/tBAgQIECAAAECBAgQIECAAAECBAiMUEABdIS4uiZAgAABAgQIECBAgAABAgQIECBAYLwCCqDj9bd2AgQIECBAgAABAgQIECBAgAABAgRGKKAAOkJcXRMgQIAAAQIECBAgQIAAAQIECBAgMF4BBdDx+ls7AQIECBAgQIAAAQIECBAgQIAAAQIjFFAAHSGurgkQIECAAAECBAgQIECAAAECBAgQGK+AAuh4/a2dAAECBAgQIECAAAECBAgQIECAAIERCiiAjhBX1wQIECBAgAABAgQIECBAgAABAgQIjFdAAXS8/tZOgAABAgQIECBAgAABAgQIECBAgMAIBRRAR4irawIECBAgQIAAAQIECBAgQIAAAQIExiugADpef2snQIAAAQIECBAgQIAAAQIECBAgQGCEAgqgI8TVNQECBAgQIECAAAECBAgQIECAAAEC4xVQAB2vv7UTIECAAAECBAgQIECAAAECBAgQIDBCAQXQEeLqmgABAgQIECBAgAABAgQIECBAgACB8QoogI7X39oJECBAgAABAgQIECBAgAABAgQILE9gzeW9YXr/Aqv3P6s5CRAgQIAAAQIECBAgQIAAAQIECBAYscAa6X/v5MDkSSNe10x0rwA6E4fZThIgQIAAAQIECBAgQIAAAQIECEywQJ3peUiyR/LsxJmfQRhWUwAdlqR+CBAgQIAAAQIECBAgQIAAAQIECPQvsFZmrTM9D0qq6Flnfjbtgox8MNkh+aNEW4SAAugi8CxKgAABAgQIECBAgAABAgQIECBAYACBKnruk1TR85lJu+h5fl5X0fONyUVJtRPuGvjvYgQUQBejZ1kCBAgQIECAAAECBAgQIECAAAECKxZYO2+3i57LWrOfl/Eqer4pubg13egQBRRAh4ipKwIECBAgQIAAAQIECBAgQIAAAQIRWCdpip6HZ7xd9PxRXjdFz0syro1YQAF0xMC6J0CAAAECBAgQIECAAAECBAgQmAmBdbOX+yZ1efszknbd7dy8PjGpMz0vTbQlFGgfiCVcrVURIECAAAECBAgQIECAAAECBAgQ6LxAFT33S6roeVjSrrX9MK/rTM83J5cl2pgE2gdlTJtgtQQIECBAgAABAgQIECBAgAABAgQ6I7BetnT/5MCkip6rJU37QUaaouflzUTD8QoogI7X39oJECBAgAABAgQIECBAgAABAgQmX2D9bGIVPetMz6cn7aLn9/O6ip5vSa5ItAkTUACdsANicwgQIECAAAECBAgQIECAAAECBCZCYINsRbvouWprq87OeFP0vLI13egECiiATuBBsUkECBAgQIAAAQIECBAgQIAAAQJjEdgwa31oUmd6PjVpFz2/l9dV9HxrougZhK40BdCuHCnbSYAAAQIECBAgsFCBNbLg7yT1gIKtkhuS85JPJhckGgECBAgQIDDbAhtl99tFz1V6HL/I8LtJFT2PSa5KNAIECKxU4FuZo36BfHilc5qBAAECBAgQILA4gfrycmRycVKfP+bLf2b6jolGgAABAgQIzJbAxtndxyXHJ3cmzeeEGj8jeXlShdFxtxOyAbVth457Q7q8fmeAdvno2XYCBAgQIECAAIHlCayVN/4teVJvhjp74xPJT5J1kwcn9aXnCUmdHXpQ8vlEI0CAAAECBKZXYJPs2gFJ/bt/SGs3m6LniZlWZ3pe03rPKAECBAYWcAbowGQWIECAAAECBBYgUMXPOlui7s/VFEHndrNFJnwgqfluSB6YaAQIECBAgMB0CVTRs/7g2Xw2aM70vCPTqkbx0mSDZFKbM0An9cjYLgIrEFAAXQGOtwgQIECAAIGhCByYXurLTZ29cf8+enxHb/46S7T9oIM+FjULAQIECBAgMKEC9QfQf0+agmcNb09OT16SrJ90oSmAduEo2UYCcwQUQOeAeEmAAAECBAgMXeCs9Fhfcp7VZ8/1kKQf95b5oz6XMRsBAgQIECAweQL17/hJydyi52mZdnSyXtK1pgA6hCPmHqBDQNQFAQIECBAgQIDAxAjcO1uya3J58u4+t+rWzPfG5E1JnT36oUQjQIAAAQIEuiFQ/3a/IHlYa3PrTM9vJ/X09rcn1yftVn/8fERy36QedHRZUvOfmlTxVCNAgMCiBJwBuig+CxMgQIAAAQIrEfjjvF9fXOoLzyDtfpm5ljtnkIXMS4AAAQIECCy5wCpZ45OTLyftMz1vy+tvJEcl6ybztXUy8RXJ1Ul72Wb8p5l+eFLrmJTmDNAhHAlngA4BURcECBAgQIAAAQITI7B5b0suHnCLLunN3yw/4OJmJ0CAAAECBEYoUPfoPiipMz33b62nip51T8/6w+exyY3J8tq2eeNjyQN6M9QZn19NrkrunvxuskPyzuTxySHJ3DNHM0kjQIDAygWcAbpyI3MQIECAAAECCxeoLyt1Fkc96XWQtnNmruX+e5CFzEuAAAECBAiMTKBO2js4+VrSnKFZw7p1TU17cbJ20k+ry9x/mNTyZyf7JfO1OrO0bqNT830iqcLruJszQMd9BKyfwAIEFEAXgGYRAgQIECBAoG+BPTJnfWmpS9gGaXW5Wy330UEWMi8BAgQIECAwVIFl6e1PklOS+ne5yS0Z/0ryoqTfomdm/VU7LmPVV9UkNvjV1PlHdsrkS5Oa/3nzz7KkUxVAl5TbyggMR0ABdDiOeiFAgAABAgSWL3BB3qovLU9c/iy/8U7d5+s7SS1z2G+84wUBAgQIECAwaoF6IFFdwVH376x/i5vcnPEvJy9I1koW2uoqjzuSKqLWJe79tLoEvrajbpFTRdlxNgXQcepbN4EFCiiALhDOYgQIECBAgEDfAkdkzvrScmFS9/RaWfvrzFDzX5CsmWgECBAgQIDAaAWqoPnU5LSkKXjWsIqeJyfPT4b1b/JL01f1/e5kkHZmZq7lfm+QhUYwrwLoCFB1SWDUAgqgoxbWPwECBAgQILBaCL6Y1JeW85IHJvO1+mL16qTmuz35/UQjQIAAAQIERiNQl64/LflmUv/2Nrkp4yclz02GVfRMV79qH85Yravu7zlIe01mruVePshCI5hXAXQIqHVDWY0AAQIECBAgQIDANAnUZW4HJp9O9k7q6bB1b896mMFPknWTByd15sm2yW3JEcnnEo0AAQIECBAYnsA66aqe3v7CZM9Wt1X0rEve6+nt70rqwUajalv2Oq4rQwZpzfzN8oMsa94JE1AAnbADYnMIECBAgAABAgSGInBlenl48qqk7h1W9wOtzG1nZkJdZvfVuW94TYAAAQIECCxIYL0sVUXP+vf3ga0ebsx4U/Ssy9FHWfRsrfZu1/ZebNCe2Md4M3+zfB+LmGVSBRRAJ/XI2C4CBAgQIECAAIHFCtR9xI5O3pBU8XO/ZKvkhuRHySeTLyV3JhoBAgQIECCwcIH1s2gVPV+Y7N7qpoqeX0/qTM/jkrrqYqnbuVnhHyb7Jp8ZYOU1f7VaXiNAgMBAAu4BOhCXmQkQIECAAAECBAgQIECAwEQKbJitOjypqynqXplNrs/455JnJZNw4t3v9ratboPT7z1G62nxtyZ1j/DNknE29wAdp751j1yg7jHxO8nByR7JsmQamgLoNBxF+0CAAAECBAgQIECAAAECsyiwUXa6CptnJU3Bs4bXJXV25TOTSSh6ZjN+1VbJ2LeT2s66KmRlrbb/C0nN/86VzbwE7yuALgGyVQxXYNV0d5/kkOSwpH0vjLz8Zbtn/nt8Un9laP8yuSWv35NskHS5KYB2+ejZdgIECBAgQIAAAQIECBCYNYGNs8PPTr6XtOsUdW/MTyfPSFZLJrntk42rukpt/z8lyzvJrAq8H+/N9/MMt0rG3RRAx30ErH8ggTqL8/tJ+5dFjddp4fXLpNo9kvOSufO0X1+Q9x+UdLUpgHb1yNluAgQIECBAgAABAgQIEJgVgU2zo0cmZyftmsQ1ef2ppE7qmvSiZzbxN1pdYdsUQf8743+ePCTZJXl48vfJ5Unt72XJXskkNAXQSTgKtqEvgcdnruZ/svYvjma8noJWZ4d+Pmmm1V8a3p+8OvlAcnHSvPejjK+ddLEpgHbxqNlmAgQIECBAgAABAgQIEJh2gbrX5XOSc5Km/lDDKnp+Inl6UrWLLrf9s/Fzi7rtfa3x/0q2n6CdVACdoINhU5YvsH7eqmJm8z9UFTv/IXlNcmZr+ptb4/8v4+sm7VaXvh+XNP3UXya62BRAu3jUbDMBAgQIECBAgAABAgQITKPA5tmp5yY/SJp6Qw2vTupS8KclXS96Zhd+o9WZq09IqsZSNZofJl9J3pQckExaUwCdtCNie+YVeGWmNr9EXprxuvlu0+rGusckzfs1/Ejz5jzDWvZLSc13XdLuKy870RRAO3GYbCQBAgQIECBAgAABAgQITKlAPXT5+UkV/tr1iKvy+mPJU5Mu1huy2VPZFECn8rBO3059NrtUv1Dq8vb52hqZWJe0N790dphvpta0/Vrz3qs1vSujCqBdOVK2kwABAgQIECBAgAABAgSmRaAe5vOC5NykqT/U8MqkTsQ6JFH0DMIENgXQIRyUOgNRG63A/Xrd1/0y5mu3ZuKXkh2TK5IfJytqZ+TNO5M6Bb36/mmiESBAgAABAgQIECBAgAABAgTaAlvnxYHJC5OqOTStip5fTj6YvC+pQqhGYKoFFEBHf3g37K2ibhq8vHZ974063byfdkdmqgLoev3MbB4CBAgQIECAAAECBAgQIEBgJgTukb08KKmzPXdo7XGdcHVycmJSRU+NwEwJKICO/nDXPTUelOyVvCeZr+3Zm1i/nNZJbpxvpt60emLZst54PZlNI0CAAAECBAgQIECAAAECBGZX4J7Z9abouX2L4fKMV9GzzvR8f2u6UQIECAxd4Pj0WKeT35zcd57e/3fv/eYeHC+aZ572pHf05r8tw7p/aNfat7LBta8f7tqG214CBAgQIECAAAECBAgQIDAhAvVMkKOS85OmntAMq+D55ESbDgH3AJ2O4zj1e/Hg7GFdsl6/iOoS9+ckVQh9SPJ3Sd0DtN47vTe8IcOHJfO1mr/5hfbx+WbowDQF0A4cJJtIgAABAgQIECBAgAABAhMnsG226M+TC5KmNlDDek5IneH58ESbPgEF0Ok7plO7R2/LnrV/Oc0dr3txbJ5c3Juvfnm9M3lKUr/Ajk4+nzTLVZF0u6SLTQG0i0fNNhMgQIAAAQIECBAgQIDAOAS2y0qrJvDTpKkJ1LBOtPqP5IBEm24BBdDpPr5TtXd1qfrrkipstn9h1fi1yX5JtSp4zjdPe5n6JVdnkXa1KYB29cjZbgIECBAgQIAAAQIECBBYCoF6PshLkp8l7XpA3QqvHmC0f6LNjoAC6Owc66nZ032zJ3+b1OXrlVcmWyXt9sy8uDpp/5Jrxs/P9Ie1Z+7guAJoBw+aTSZAgAABAgQIECBAgACBkQrsmN5fmlyYNDWAGtZt8/4taU6cyqg2YwIKoEM44KsPoQ9d9C9wSmatrKjVpe8nJocmda/QTZOzkzOSk5LrE40AAQIECBAgQIAAAQIECBDotsDO2fwDk+cnW7d2pYqe9SCjtybfaE03SoDAAgUUQBcIN+LF6gzQ+kWnESBAgAABAgQIECBAgAABAtMjsEt25aDkecndW7t1c8ar6HlMcmprulECBIYgoAA6BERdECBAgAABAgQIECBAgAABAgSWI3DvTG+Knu3b4N2U6c2Znt9czrImEyAwBAEF0CEg6oIAAQIECBAgQIAAAQIECBAg0BKoW9pV0fO5yZat6TdmvCl6nt6abpQAgREKKICOEHcEXS9Ln+1fnBeOYB26JECAAAECBAgQIECAAAECBAYXuF8WaYqeW7QWr2d5NEXPb7emGyVAYIkEFECXCHpIq3lA+mn/hWiVIfW7sm6OzgwvToaxvs16K9toZSv1PgECBAgQIECAAAECBAgQmHCB+2f7mqLn5q1tvS7jTdHzO63pRgkQGIOAAugY0Du4yp2yze0n0g1jF9YcRif6IECAAAECBAgQIECAAAECSyywW9ZXRc/nJM1JPrUJ1yQnJm9Jzkw0AgQmREABdEIOxIRvxpHZvr9OVh3Cdn42fdQ/FpcMoS9dECBAgAABAgQIECBAgACBUQvU1ZDtouemrRVenfHmTM/vtqYbJUBgggQUQCfoYPSxKfUXpPYT4/pYZCiz/CK9DKtgedtQtkgnBAgQIECAAAECBAgQIEBgdAJV9Nw9OTCpMz03SZp2VUaaoudZzURDAgQmV0ABdHKPzXxbdnsmDqsQOV//phEgQIAAAQIECBAgQIAAgVkVqKLnHkld3l5XQm6cNO2KjDRFz7ObiYYECHRDQAG0G8fJVhIgQIAAAQIECBAgQIAAAQLDF6hbvbWLnu0H9l6e95qi5/eHv2o9EiCwVAIKoEslbT0ECBAgQIAAAQIECBAgQIDAJAhU0XPPpM70fHbSLnpeltdN0fOcjGsECEyBgALo+A9iPV297iWyTi83Z1hPjrs2qVPs67VGgAABAgQIECBAgAABAgQILFxgtSzaLnpu2OqqbjXXFD1/2JpulACBKRFQAF36A7l+Vvm05JBk16ReL6/VPT/rhsqnJp9IPpXUA4k0AgQIECBAgAABAgQIECBAYMUCVfTcK2nO9NygNfvFGW+Knue2phslQIAAgUUIbJllj0nqzM4qYi4kVQx9bNLl9q1sfO37h7u8E7adAAECBAgQIECAAAECBCZSoE702id5fTL3+/fPM+1Nyc6JRqArAidkQ6uOcmhXNngSt9MZoEtzVOrJcZ9Pdmutrn54L0p+mlyW3JTcktQxWSupv0xtk2ybrJlUqzNGP5Yclbwx0QgQIECAAAECBAgQIECAwKwL1PfoByd1puezkvWSplXRs870rBOSftRMNCRAgACB4Qqsm+6+nlTBs3JacnCyedJPW5aZ9k+OTW5Nmn4ek/EuNmeAdvGo2WYCBAgQIECAAAECBAhMlkDzXfmfs1nXJc135Rr+LHlDskOiEei6gDNAu34EZ2T7D8t+Nr+I35fxetrcQlsVPZsi6Hczvpi+FroNi11OAXSxgpYnQIAAAQIECBAgQIDAbAqskd1+aFKXsV+fNN+1a/iT5HXJ9olGYJoEFECn6WhO8b68I/tWv4zPTOovVIttL0wHzS/5HRfb2RiWVwAdA7pVEiBAgAABAgQIECBAoKMCVfQ8IHlzckPSfB+u4QXJa5PtEo3AtAoogA7hyLoH6BAQV9JFXb5e7ePJbb8cW9x/PpTF669d1XZJzvvlmP8QIECAAAECBAgQIECAAIHpEKjnYNSDjOqens9I1k6adkFGmnt61lmfGgECBFYqoAC6UqJFz3DPXg8/W3RPd3VwRQZVSK2zSdv/CNz1rv8SIECAAAECBAgQIECAAIHuCdTDgJui52EZb3/f/XFeV9Hz/yU/TTQCBAgMJKAAOhDXgmauMzT3SPZN6kFGi237pYPmUvrvLLYzyxMgQIAAAQIECBAgQIAAgTEJVNGzvivXmZ5V9KzXTavv0k3Rc1gnFDV9GxIgQIDAkAXemf7q3iQ3JQ9fZN8bZfkqelZ/dSZoF5t7gHbxqNlmAgQIECBAgAABAgQIDEegzux8VPL25Oakvt82OTfj/5DcI9EIELhLwD1A/SR0QmDHbGXz5ParM35EUjdxHrTVWaSnJc0/DH8/aAcTMr8C6IQcCJtBgAABAgQIECBAgACBJRJYJ+v53aSuipxb9Pxhpv1dsnWiESDw2wIKoL9tMvAUl8APTDbwAnXa/suSejLdhkn9lavGT07OSM5PLknqDNH6h6COSZ32v0GyTbJT8rBk16Rpn8vIXzUvDAkQIECAAAECBAgQIECAwIQJVNHzocmBydOT9olAVfRsLm+/KOMaAQIECEyJQN3P5MakOYNzocNPp49NOmziDNAOHzybToAAAQIECBAgQIAAgRUIrJv3/iCpW8HdkrS/934/r/822SrRCBDoX8AZoP1bmXNCBDbPdtSl6/UXrvY/BCsbrzNDP5L8r6TrTQG060fQ9hMgQIAAAQIECBAgQODXAutl9A+TdyXN7d+a77hnZ9rfJFsmGgECCxNQAF2Y228s5RL43+AY+YvLsoaX97JdhvskOyd1uXtdHr9+cltyfXJtUpfP11/JzkxqmkaAAAECBAgQIECAAAECBMYtUN9dD0jq6e2HJMuSplXRsy5vf1tyaTPRkAABAuMUUAAdn/4FWXVFI0CAAAECBAgQIECAAAECky5QRc96PkVT9GzXE87K9Cp6vj2pE380AgQITJRA+xfWRG2YjSFAgAABAgQIECBAgAABAgTGKlBXKzZFzz/JeFNDqEvcv5s0Rc/LM64RIEBgYgWaX14Tu4E2jAABAgQIECBAgAABAgQIEFgygbo928OTOtPzKclqSbUqep6RnJjUmZ5XJBoBAgQ6IaAA2onDZCMJECBAgAABAgQIECBAgMDIBDZKz03R8+CMt4ue38nrOtPz2OTKRCNAgEDnBBRAO3fIbDABAgQIECBAgAABAgQIEFi0wMbp4RHJgUkVPVdNqt2ZfDupoue/JIqeQdAIEOi2gAJot4+frSdAgAABAgQIECBAgAABAv0KbJIZH5HU5e1PTtpFz9Pzuoqe70iuSjQCBAhMjYAC6NQcSjtCgAABAgQIECBAgAABAgR+S2DTTHlE0hQ9V+nNcUeG30yaoufVvekGBAgQmDoBBdCpO6R2iAABAgQIECBAgAABAgRmXGCz7P/vJFX0rEvc20XPb+V1U/S8JuMaAQIEpl5AAXTqD7EdJECAAAECBAgQIECAAIEZENg8+9gUPf8o403R8/aMN5e3vzPj1yYaAQIEZkpAAXSmDredJUCAAAECBAgQIECAAIEpEtgi+9Iueja7VkXP5vL2Knpe17xhSIAAgVkUUACdxaNunwkQIECAAAECBAgQIECgqwJbZsMfmdTl7U9s7cRtGT8tOTF5V6LoGQSNAAECJaAA6ueAAAECBAgQIECAAAECBAhMtsCybF4VPCtPaG1qFT1PTeqenu9Ork80AgQIEJgjoAA6B8RLAgQIECBAgAABAgQIECAwAQJrZhuq4HlE8tDW9tya8XbR84bWe0YJECBAYB4BBdB5UEwiQIAAAQIECBAgQIAAAQJjEFgr66yi55HJfq3135LxbyR1pudxyY2JRoAAAQJ9CiiA9gllNgIECBAgQIAAAQIECBAgMAKBtdNnU/Tct9V/FT1PSaro+Z5E0TMIGgECBBYioAC6EDXLECBAgAABAgQIECBAgACBhQusm0WboudDWt3cnPF20fOm1ntGCRAgQGCBAgqgC4SzGAECBAgQIECAAAECBAgQGEBgvczbFD33bi1XRc6vJ3Wm578mVQTVCBAgQGCIAgqgQ8TUFQECBAgQIECAAAECBAgQaAlskPEDk+ckD2pNr6Ln15Iqeh6fKHoGQSNAgMCoBBRARyWrXwIECBAgQIAAAQIECBCYRYENs9PNmZ57tQDqHp5fTU5MquhZ9/jUCBAgQGAJBBRAlwDZKggQIECAAAECBAgQIEBgqgU2yt5V0bPO9Hxga09vyHgVPetMzxOSWxONAAECBJZYQAF0icGtjgABAgQIECBAgAABAgSmQmCT7EVzpucerT2qoudXkip6vjdR9AyCRoAAgXEKKICOU9+6CRAgQIAAAQIECBAgQKBLAptmY5ui5+6tDb8+419Oquj5b8ltiUaAAAECEyKgADohB8JmECBAgAABAgQIECBAgMBECmyWraqiZ13evltrC6/LeFP0/PeMK3q2cIwSIEBgkgQUQCfpaNgWAgQIECBAgAABAgQIEJgEgS2yEc2Znru2NujajLeLnre33jNKgAABAhMqoAA6oQfGZhEgQIAAAQIECBAgQKFloxsAAEAASURBVIDAkgpsmbU1Rc/7t9Z8TcZPTury9v9IFD2DoBEgQKBLAgqgXTpatpUAAQIECBAgQIAAAQIEhilw93R2YFKXt9+31fHVGW8XPe9ovWeUAAECBDomoADasQNmcwkQIECAAAECBAgQIEBgUQJbZ+nmTM/7tHqqoudJyYnJ+xNFzyBoBAgQmAYBBdBpOIr2gQABAgQIECBAgAABAgRWJHCPvNkUPe/dmvGqjFfRsy5v/0ByZ6IRIECAwJQJKIBO2QG1OwQIECBAgAABAgQIECDwS4Ft8t+m6Llzy+TKjDdFzyp8Knq2cIwSIEBgGgUUQKfxqNonAgQIECBAgAABAgQIzKbAvbLbTdFzpxbBFRn/YlIFzw8lip5B0AgQIDArAgqgs3Kk7ScBAgQIECBAgAABAgSmU2Db7FZT9NyxtYuXZ7xd9PxF6z2jBAgQIDBDAgqgM3Sw7SoBAgQIECBAgAABAgSmRGD77EcVPY9Idmjt02UZb4qeH864omcLxygBAgRmVUABdFaPvP0mQIAAAQIECBAgQIBAtwSq0Nmc6blda9MvzfgXkrq8/SOJomcQNAIECBD4tYAC6K8tjBEgQIAAAQIECBAgQIDAZAnslM05MDkyqUvdm3ZJRtpFz2a6IQECBAgQ+C0BBdDfIjGBAAECBAgQIECAAAECBMYoUE9sby5vv1drOy7O+H8lJyYfbU03SoAAAQIEViigALpCHm8SIECAAAECBAgQIECAwBII7JJ1NEXPbVrruznjdWl75eOt6UYJECBAgEDfAgqgfVOZkQABAgQIECBAgAABAgSGKHCf9FVFz2cn92z1e1PGq+D5L8nXWtONEiBAgACBBQkogC6IzUIECBAgQIAAAQIECBAgsACB+2aZpuh5j9byN2S8KXqe0ppulAABAgQILFpAAXTRhDogQIAAAQIECBAgQIAAgRUI3C/vNUXPrVvzXZ/xKnoem5zamm6UAAECBAgMVUABdKicOiNAgAABAgQIECBAgACBCOyaVNHzWcndk6Zdm5F6iFEVPU9rJhoSIECAAIFRCiiAjlJX3wQIECBAgAABAgQIEJgdgd2yq03Rc6vWbl+T8eZMz9Nb040SIECAAIElEVAAXRJmKyFAgAABAgQIECBAgMDUCaySPXpAcmBSZ3pumTTt6ow0Rc9vNRMNCRAgQIDAOAQUQMehbp0ECBAgQIAAAQIECBDopkAVPXdP6kzPZyZbJE27MiPNg4y+3Uw0JECAAAEC4xZQAB33EbB+AgQIECBAgAABAgQITLZAFT33SJqi5+atzb0i482Znme0phslQIAAAQITI6AAOjGHwoYQIECAAAECBAgQIEBgYgRWzZY8MKmi5+HJZknTLs9IU/Q8s5loSIAAAQIEJlVAAXRSj4ztIkCAAAECBAgQIECAwNIKVNFzz6Qpem7aWv2lGW+Knme1phslQIAAAQITL6AAOvGHyAYSIECAAAECBAgQIEBgZAJV9NwraYqem7TWdEnGm6Ln91rTjRIgQIAAgU4JKIB26nDZWAIECBAgQIAAAQIECCxaYLX08KCkip7PSDZOmnZRRk5Mjk3ObiYaEiBAgACBLgsogHb56Nl2AgQIECBAgAABAgQI9CdQRc8HJ03Rc6PWYv+T8eZMz3Na040SIECAAIGpEFAAnYrDaCcIECBAgAABAgQITJTAetmaxyQPS7ZObk4uSD6dfDX5RaKNXqC+7+2dHJjUmZ4bJk37eUaaoucPmomGBAgQIECAAAECixf4VrqoD7wfXnxXeiBAgAABAgQIEJgwgVWyPS9OrkjqM998OSPTH55ooxGoouf+yRuTq5P2MfhpXr8+uXeiESBAgEA3BE7IZtbv8kO7sbmTuZXOAJ3M42KrCBAgQIAAAQIECHRNYM1s8H8kT+ht+Ncy/EhyXrJWskdycLJ78oXkBcnbEm3xAsvSxUOSurz9T5MNkqZV0bPO9PyX5NxmoiEBAgQIECBAgMDoBJwBOjpbPRMgQIAAAQIExinwr1l5naFyeVKXv8/Xqkj6quTOXp4430ym9SVQRc+6xcBbkmuT9pmeF+T1a5OdEo0AAQIEui3gDNBuHz9bP6MCCqAzeuDtNgECBAgQIDDVAo/O3lUB7rpktz729M9681+a4fp9zG+WuwTWyODhyVuTsm4XPX+c169Jdkw0AgQIEJgeAQXQ6TmW9mSGBBRAZ+hg21UCBAgQIEBgZgTqcvcqxr1ogD3+Um+ZowZYZhZnrbNmH5Eck8wtetbtBf4x2SHRCBAgQGA6BRRAp/O42qspF1AAnfIDbPcIECBAgACBmRPYKntcl7TfkKw9wN7XvUKraFrFU+03Baro+cik7pF6fdI+0/O/8/rVyfaJRoAAAQLTL6AAOoRj7CFIQ0DUBQECBAgQIECAAIEZFrhf9r2e/n5qctMADl/qzbvrAMtM86z1oKh6ens9yOipyTpJ06roWQ8yekdyQaIRIECAAAECAwgogA6AZVYCBAgQIECAAAECBH5LYNPelHr40SDt6sx8e1JPLK/vJTU+a63OmH1ocmByaNIuetYT25unt9eT3DUCBAgQIEBggQIKoAuEsxgBAgQIECBAgAABAr8UaAqfWwzosXHmr+8j1ySzVPysoucBSZ3peUjSvm3AD/K6OdPzZxnXCBAgQIAAgSEIKIAOAVEXBAgQIECAAAECBGZY4Ozse90DdO9k3aTuBdpPq3tcVvvuXYOp/m+d2dkuetbl7k07JyNN0fPCZqIhAQIECBAgQIBAdwU8BKm7x86WEyBAgAABAgSWJ3By3qgH9Ry9vBnmmd48Of7F87w3DZOqGPzo5N1J3Ru1/SCjKhr/TXKPRCNAgAABAisS8BCkFel4j8CECiiATuiBsVkECBAgQIAAgUUI/G6WrQJfnf25Vx/9vKw3/0UZVqGwaXU/0Ho6/J8lL0nqYUDbJl1ptS+PSY5Lbk7aRc+z8vqvk60TjQABAgQI9CugANqvlPkITJCAAugEHQybQoAAAQIECBAYosCx6asKfvVwo3qoz3ytLgV/XVLz3ZFUsbBanQlZZ0rekrSLhs14nWG6bzKJbb1s1GOT9yRzt78u7/+r5O6JRoAAAQIEFiKgALoQNcsQGLOAAuiYD4DVEyBAgAABAgRGJLAs/b4vaYqW9bmvin/1oJ9nJG9O6ozPev/W5LCk2iOSepBSTb8t+ULyhuQfkw8m9ZCkeq8KpnVW6CS09bMRj0uOT+YWPc/ItL9Mtko0AgQIECCwWAEF0MUKWp7AGAQUQMeAbpUECBAgQIAAgSUUOCLrujhpCqFzh6fkvYf0tmfPDOuy+ZrnE8n2ydxWl5X/XVIF0JrvRck4Wl2e//ikvohWAbfZr3oA1HeSuqx/y0QjQIAAAQLDFFAAHaamvggskYAC6BJBWw0BAgQIECBAYIwC9ZTzOkPyn5L3Ju9K6qzI9v1BV8/rHyZVSHxnskqyovbHebOKjbcn91vRjEN8r7knae3D3KLntzPtL5Ithrg+XREgQIAAgbkCCqBzRbwm0AEBBdAOHCSbSIAAAQIECBBYAoG6LL6Kn99P6vL5ftpbM1Mt84F+Zl7gPBtmuScm/57UJfnNmZ51BurpSV2Gv3miESBAgACBpRBQAF0KZesgMGQBBdAhg+qOAAECBAgQINBRgc9mu6u4+LQBtr/uq1mFyBuTdQZYbmWzbpQZnpTUPUznFj2/mWn/N9ks0QgQIECAwFILKIAutfgK1lcfGF6RbLeCebxFoAQUQP0cECBAgAABAgQIlEA9Lb4KoIMWFpvPk/tUJ4toG2fZA5P3J3VZfftMz9Py+uhk00QjQIAAAQLjFFAAHaf+nHXXzb7rA0Pdk+ek5OlJ3axcIzBXoPnA+uG5b3hNgAABAgQIECAwMwJ1j9D6/nDTAvb4I71l//cClt0kyxyU1CX07aJnjX8jOSqpeTQCBAgQIDApAgqgQzgSdePxYba6cfkjejkmwxOT9yQnJ/UBRyNAgAABAgQIECBAgMAtIaiHCq2ZrNEbz6Cvtn5vruv6mvuuszgflXmr8Fn39lytt1xdSl9Fzw8mxyVXJRoBAgQIECBAYLkCq+ad+gvsh5L6MFPFznbOz+u/SXZItNkWcAbobB9/e0+AAAECBAgQaATOzkh9ZzigmdDHsB6W1Fw6v80K5q/L6g9O6vtJFTqb7yZ1f8+vJX+W1CXwGgECBAgQmHQBZ4BO6BGqS0aek5ySNB80mmFdIl9ngx6WrJdosyegADp7x9weEyBAgAABAgTmE/jHTKzvCe+d783lTDu0t8wZ87y/eaY9JalbLc0ten41016UbJRoBAgQIECgSwIKoB04WjtnG1+VnJ80RdBmeH2mHZ88MqlL57XZEFAAnY3jbC8JECBAgAABAisTqDM46x6gdZLEY1Y2c97fOvmfpL5PVCG02hbJIcl/JtVP812jLq//SvLCZMNEI0CAAAECXRVQAO3QkasC58OSdySXJM0Hk2Z4Qaa9Mtk+0aZbQAF0uo+vvSNAgAABAgQIDCLwksxc3wnq5IgnrWDBe+e9c5Ka98tJFUA/mswtep6cac9PNkg0AgQIECAwDQIKoB09iqtmu/dLXpvckDRF0BrWB5j/Sp6QOCs0CFPYFECn8KDaJQIECBAgQIDAIgSOzbLNd4LPZvxPkvsnOyV/mNT7tyQ1T93/s130rOlfSp6XrJ9oBAgQIEBg2gQUQDt4RNfONj8+eXdyWdJ80JlvWIWyeyXadAkogE7X8bQ3BAgQIECAAIFhCFQB86pkvu8Fc6dV0fOk5LmJomcQNAIECBCYagEF0I4c3tWynb+fHJ9cl8z9AHNFpr0l+YPktclFSTPPxRl/cKJNj4AC6PQcS3tCgAABAgQIEBimQD1M9WVJPeDo2qT5TlDDKnp+ITky8TDVIGgECBAgMDMCCqATfqj3zPa9IWkXNJsPMbdn+qeSg5I1k3Zblhd/nzTz1n18tOkRUACdnmNpTwgQIECAAAECwxC4Rzo5LKnvB813gBrWA5Lq9lhHJOsmGgECBAgQmEUBBdAJPOrbZpvqr7bfT9ofXprxH2b6S5P6kLOy9rXMUMvdlszaTczrrNldknoa5r7JVsm0NAXQaTmS9oMAAQIECBAgsHCB+nx/ePKZpPmuUMMqen4ueXayTqIRIECAAIFZF1AAnaCfgPWzLfU0xvYNyZsPMnX5Sj39fb9kkPbPmbnp4/6DLDjB8z4y2/bm5J3L2cbdMr0u7bk5afa9GZ6aac9K6iFSXW4KoF0+eradAAECBAgQILBwgQ2z6DOTU5LmM24Nb0w+m9R7ip5B0AgQIECAQEtAAbSFMe7RLbMB7Q8xVQj9YvLUZKEfYo7r9VnFwNWTLre1svH/kjRGdV+jue1VmVBnuzbzLG/4lcxzz7kLd+i1AmiHDpZNJUCAAAECBAgsUmDjLF9nc9Yf89ufb6voWWd/Hp7Ug1I1AgQIECBAYH4BBdD5XcYytSmAnp+1/02y/RC24kHp4wFJ/aW46+1D2YH2B74fz9mh+mt3+/3L8vrzyduS/0iqaHhH0sxzZsa7eh8kBdAcPI0AAQIECBAgMMUCm2Tf6r6dpyXN59ca3pDUfT7rfp91goBGgAABAgQIrFxAAXTlRks2RxXj6vLuVZZsjd1Z0aOyqc0Hv59n/NCkXbzcKa+v781ze4avSuY7a3aPTP9Kb77q73VJF5sCaBePmm0mQIAAAQIECKxYYNO8XU9oPz1pPvvWsD7nfjL500TRMwgaAQIECBAYUOCEzF//plY9SSMwsQLN2Z/1F+/7zLOVf5FpzYfEV8zzfntSfWj8Tm/+qzKcr1Dann8SxxVAJ/Go2CYCBAgQIECAwOACm2eR5ybN57vmM+11mfaJ5OnJmolGgAABAgQILFxAAXThdpZcQoGzs676MPim5azzxN77ddn7asuZpz35gN781ec+7Tc6Mt58QP5wR7bXZhIgQIAAAQIECPxaYIuMPi/5dtIUPGtYRc+PJfUMAEXPIGgECBAgQGBIAgqgQ4Ds+sOFhkAw8i627a2hztycrzX3S63CYN3nc2Wt7qVUD0tallTf30g0AgQIECBAgAABAqMS2CodH5jUfet3b62kip4nJR9MPpDcmmgECBAgQIAAgYkTUAAd/SH5UVZRHxR3W86q6j5Jey7nvfkmb5aJVfysduldA/8lQIAAAQIECBAgMFSBu6e3g5LDk3owadOuzcgXk7qKqQqfip5B0AgQIECAAAECsy7wzgDUZUFzn/zeuBzSe7+Kmf1cAl9P1Kz+7kw2TLrWXALftSNmewkQIECAAIFZEdg6O/qi5KykPm82uTrjdfuipyTNH+IzqhEgQIAAAQJLIOAS+CVAtorFCzw7XTQfHo+ep7u6pKg+VNY8L5/n/fake+XFD5Ka99z2Gx0aVwDt0MGyqQQIECBAgMDUC9wze/hnyfeS5jNrDa9KPpQcnCh6BkEjQIAAAQJjElAAHRO81Q4mUDeBr/t2Nh8o35rxTed08dC8vjGpS4j+TzLfmaAPyfSLk6afwzPexaYA2sWjZpsJECBAgACBaRLYJjtTnzmbh3U2ny+r6FmXtT85causIGgECBAgQGACBBRAJ+Ag2IT+BOpD5mVJ8+GyzvisH+DDkgcmdWbnHyf1cKOap87yfFfyl8l7k/OSZtkavifpalMA7eqRs90ECBAgQIBAlwXq8+ZRyTlJ+3PllXldDzCq+30qegZBI0CAAAECEyagADphB8TmrFigzuCsy9bbHzgXMn5y+lhnxaua6HcVQCf68Ng4AgQIECBAYIoEtsu+1C2YmlsoNZ89r8i09yf1ZPfVEo0AAQLTLFDfn5+TfCb5SVIPc6uTjOphbnWbD78Hg6BNtIAC6EQfHhs3n0BdDl+XG52RNB9A+x1+P8scmaySdLkpgHb56Nl2AgQIECBAYNIFts8G/t/kh0n7c+blef2+5EmJL/tB0AgQmAmBx2cv/ydp/z6cO163A9lzJjTsZFcFFECHcORc5jIExAG6uCXzvqGXXTLcK9k12SHZIFkvWSO5IbkuuTA5Kzk1OTPRCBAgQIAAAQIECMwV2DET6mzOw5OdW29W0fPzSd3X86PJnYlGgACBWRF4Xnb0LUmdRPSNpJ7H8ZWk7ne8VfJ7ST0E7n7JV5MnJJ9LNAIECBAgsGgBZ4AumlAHBAgQIECAAIG77RSDv0h+lLTPZro0r9+b1Bf5VRONAAECsyjwqOz07Un94eeoFQAsy3vHJvV7tJ7VUX9Q0ghMmsAJ2aD6GT100jbM9hAgsHwBBdDl23iHAAECBAgQILAigTq782XJ3AdkXpJp9eWoLvVU9AyCRoDATAuslr2vW8hVweiv+5T4QG/+D/U5v9kILKWAAuhSalsXgSEJKIAOCVI3BAgQIECAwEwI3Dt7+ZfJj5P2mZ4X5/XxyeOSrt8jPrugESBAYGgCj05P9fuyHkK8ep+9bpn5rk9quW36XMZsBJZKQAF0CNL9/jIYwqp0MQSBOj2/fjE37cJmxJAAAQIECBAgQGBqBO6TPTkoeUayXdK0Knp+Nql7en4qqS/qGgECBAj8psBjey/rj0R1GXw/rc6k/2Ty5OQxSV0WrxEgMEUCCqDdOpgPyOae3trkpfpr/1OzziOSYVxSVQ9/qlYPfNIIECBAgAABAgTuErhvBk3Rc9sWykUZb4qen864omcLxygBAgTmEdihN62uPhyk1XftKoDuOMhC5iVAoBsCCqDdOE7j3sr6C9r+Q96IDYfcn+4IECBAgAABAl0TuH82uIqehyX3am38/2S8XfRsvWWUAAECBFYisG7v/RtWMt/ct2/sTVhn7hteEyDQfQEF0O4fw6XYg7r86o3JMM44PS791L2sfp5oBAgQIECAAIFZE9g1O9wUPdv3mavPRp9JPphU8VMjQIAAgYUJ1Jnz1bZLvlwjfbbtevM1y/e5mNkIECBAYNgCVbCue4A2GXb/S9GfhyAthbJ1ECBAgAABApMkULcxemVyYVKXsDf5Wcbfkfx+ohEgQIDAcARekG7q9+yJA3RXJ/uc01vuEQMsZ1YCSyHgIUhLoWwdBIYsoAA6ZFDdESBAgAABAhMpsHu26u+SOrOzKXjW8MqkHq7xe4lGgAABAsMX2Dpd3pzckezRZ/eHZL76HV1/mFqtz2XMRmCpBBRAl0raeggMUUABdIiYuiJAgAABAgQmRqDOHqov2n+f1D0820XPK/L67cneiUaAAAECoxd4XVZRv4fPS6oguqK2Z968Nqn5/zTRCEyagALopB0R20OgDwEF0D6QzEKAAAECBAh0QqCKnvXF+dVJ3TOuXfS8PK/fljw40QgQIEBgaQXWyupOTer3cp2JX/dert/Z7bZGXrwwqYcl1XzvTTQCkyigADqEo1L3lNTGK1B/jdokqSfNVepU/WuS+gtUnS1QrzUCBAgQIECAAIHJEGiKnvVl+k+Tujd70y7LSD3E6Ljk9GaiIQECBAgsuUB9j3508oHkUb1h/aHqa0ndiuTuycOSDZNq70qe+8sx/yFAgACBoQisn16el3w9aU6zb58t0B6/LfN8O6mzBx6bzP2LVSZ1rjkDtHOHzAYTIECAAIGZF1g1Ag9KXpNckrQ/r9XrtyZ1JqhGgAABApMlsFo25/DkR0n7d3cz/s1Mr+/aGoFJFjghG1c/s4dO8kbaNgKNQJ0dcEyysqJn84t4vuFZWb7rv5wVQJufCEMCBAgQIEBgkgWq6Fn37HxtcmnS/mxWZxG9JXlgohEgQIBANwR2zWbW2fvPTp6QbJtoBLogoAA6hKPkEvghIPbRxcaZ5/PJbq1560N0fXj+aXJZclNyS1LHpO5XskGyTVK/lNdMqtUv7I8lRyVvTDQCBAgQIECAAIHhCVTR88FJfUF+erJZ0rT63PbB5N3Jmc1EQwIECBDojMD3sqUVjQABAgRGILBu+qzL3avgWTktOTjZPOmnLctM+yfHJrcmTT+PyXgXmzNAu3jUbDMBAgQIEJhegbo8ct/k9Un9Ubr5rFXDenBG/dH5AYlGgAABAgT+f3v3AW9dWd4JewApilSlKtKbimIZu4INUSxR31EnIuoUa2LKqJl0J5bJxE8TzWjUmIkRW8wrKgioWEBQI0ZRYtTYQEF6753vf+t+cHE4ZZ9z9tn1en6/P2vttVe9Fme9+9znWXsRIDAKAT1AR6Fum8sWeHGWaB+kP5zx6lmw0lZFz1YEPT3jq1nXSvdhtcspgK5W0PIECBAgQIDAagWq6PmI5C+Telp7+6xWw7OStybdO3fyUiNAgAABAgQIjERAAXQk7Da6XIG/zQL1YbpularenKttr8oK2of0PVe7shEsrwA6AnSbJECAAAECBH7xNUN1V0316Lw4aZ+nalhfSfSW5D6JRoAAAQIECBAYJwEF0AGcDd8BOgDEJVZRH7SrHZPc+Iux1f3nY1n8bb1V7JPhj1e3OksTIECAAAECBKZWoD7r1u3t9Z2e9eTU+l721qro2b7T87ttoiEBAgQIECBAgMD0CSiArv05vWdvE3U71SBa9VioQmr1Jr3zIFZoHQQIECBAgACBKRKoz0jdoufWnWM7M+NV9Pz75HuJRoAAAQIECBAgMAMCCqBrf5Krh+aBSX0Qf/cANlffV9VupT9tAOuzCgIECBAgQIDApAvUZ6P6jNR6em7VOaAzMt56ev57Z7pRAgQIECBAgAABAgQGJPDerKe+W+ra5KBVrrN6MFTRs9ZXPUEnsX0jO137f9Qk7rx9JkCAAAECBMZGYJPsyWOTdyaXJ/X5ouVHGf/zpL4uSCNAgAABAgQITLKA7wCd5LM3Q/teDypqT26/LOMvTeoD+3Jb9SI9NWkf7N+43BWMyfwKoGNyIuwGAQIECBCYQIH6DPW45G+SuUXPH2bam5K9E40AAQIECBAgMC0CCqADOJNugR8A4hKrqFvg/yB5c1K3Y72rN35Sht9KzkjOT6qH6HVJnZPNki2TXZK9ksck901a+2xG/ri9MCRAgAABAgQITLHApjm2Ryfrkl9Ptkhaq6Jn+07P6vWpESBAgAABAgQIECAwQoEXZ9vXJK0H50qHx2cd247wOFa7aT1AVytoeQIECBAgMP0CVfR8YvKe5Mqk+7np+3n9+mSPRCNAgAABAgQITLuAHqDTfoan8Pi2yzHVrevnJt0P8kuNV8/QTyRPTSa9KYBO+hm0/wQIECBAYG0E6g6YQ5K/Ta5Kup+PvpfXf5bsnmgECBAgQIAAgVkSUAAdwNl2C/wAEJexigsz7x/2sluGD0vqe6rqdve6Pb5u6boxqQ/9VyR1+/x3k28nNU0jQIAAAQIECEyTwJ1zMAcl9fT25yabJ61V0bPd3n5mm2hIgAABAgQIECBAYLkCCqDLFRvc/GdmVRWNAAECBAgQIDBLAlX0PDhpRc+7dA7+3zJeRc/3JT9NNAIECBAgQIAAAQKrFlAAXTWhFRAgQIAAAQIECCwhUEXOg5NW9KwiaGvfyUgrev6sTTQkQIAAAQIECBAgMCgBBdBBSVoPAQIECBAgQIBAV6BuZ39sUkXPSrfoeXper0/el5yVaAQIECBAgAABAgTWTEABdM1orZgAAQIECBAgMHMCVfR8XNKKnvVgo9bqO82rp+c/JGe3iYYECBAgQIAAAQIE1lpAAXStha2fAAECBAgQIDDdAnfN4T0+WddLK3rWU9y/lbTb28/JuEaAAAECBAgQIEBg6AIKoEMnt0ECBAgQIECAwMQLbJEjqKJn9fR8drJpUq2Knt9MWk/Pc2uiRoAAAQIECBAgQGCUAgqgo9S3bQIECBAgQIDA5AhsmV3tFj036e16FT2/kbSi53m96QYECBAgQIAAAQIExkJAAXQsToOdIECAAAECBAiMpUAVPZ+YVE/PZyat6HlLxv8laUXP8zOuESBAgAABAgQIEBhLAQXQsTwtdooAAQIECBAgMDKBrbLlbtFz496eVNHz1KSKnu9PLkg0AgQIECBAgAABAmMvoAA69qfIDhIgQIAAAQIE1lxg62yhFT1/LePdoufX8rqKnkcmip5B0AgQIECAAAECBCZLQAF0ss6XvSVAgAABAgQIDEpgm6zokKRub39G0j4X3pzxrybrkyp6XphoBAgQIECAAAECBCZWoH3QndgDsOMECBAgQIAAAQJ9C2ybOVvR8+kZb58Fq+j5laR6en4guSjRCBAgQIAAAQIECEyFQPvQOxUH4yAIECBAgAABAgTuIHC3THlSsi55WtI+/1XR88tJK3penHGNAAECBAgQIECAwNQJtA/AU3dgDogAAQIECBAgMMMCd8+xV9Gzbm9/arJRUu2m5OSkip4fTC5JNAIECBAgQIAAAQJTLaAAOtWn18ERIECAAAECMySwXY61FT0Py3i36PmlvG5Fz0tnyMShEiBAgAABAgQIELjtFigUBAgQIECAAAECkyewfXb50KR6ej4l2TCpdmNyStKKnpfVRI0AAQIECBAgQIDALAroATqLZ90xEyBAgAABApMsUEXPJydV9Kxht+h5Ul5X0fNDyeWJRoAAAQIECBAgQGDmBRRAZ/5/AQAECBAgQIDABAjskH1sRc/q8dmKnjdkvPX0/HDGFT2DoBEgQIAAAQIECBDoCiiAdjWMEyBAgAABAgTGR2DH7Erd1l49Peu7PTdIqlXRs77Tc31SRc8rEo0AAQIECBAgQIAAgQUEFEAXgDGZAAECBAgQIDACgZ2zzdbT85CMt6Ln9Rmvomfd3v6R5MpEI0CAAAECBAgQIECgDwEF0D6QzEKAAAECBAgQWEOBe2Td1dNzXfLEpBU9r8t4t+h5VV5rBAgQIECAAAECBAgsU0ABdJlgZidAgAABAgQIDEDgnllHu739CZ31VdHzxKR6en40UfQMgkaAAAECBAgQIEBgNQIKoKvRsywBAgQIECBAoH+BXTJrK3o+vrPYtRk/MWlFz6s77xklQIAAAQIECBAgQGCVAgqgqwS0OAECBAgQIEBgEYF75b3DknqQ0WM7812T8ROTVvSs1xoBAgQIECBAgAABAmsgoAC6BqhWSYAAAQIECMy0wK45+lb0PLgjUUXOLyRV9KwnuCt6BkEjQIAAAQIECBAgsNYCCqBrLWz9BAgQIECAwCwI7JaDbEXPgzoHXLezd4uedbu7RoAAAQIECBAgQIDAEAUUQIeIbVMECBAgQIDAVAnsmKOpW9srj+4cWT246PNJ9fKs1IONNAIECBAgQIAAAQIERiSgADoieJslQIAAAQIEJlJgp+x1FTxfmDywcwRV9PxcUre3H5UoegZBI0CAAAECBAgQIDAOAgqg43AW7AMBAgQIECAwzgL3yM5V0fOI5AGdHb0y492i5/Wd94wSIECAAAECBAgQIDAmAgqgY3Ii7AYBAgQIECAwVgL3zN60oueBnT27IuMnJNXT8xOJomcQNAIECBAgQIAAAQLjLKAAOs5nx74RIECAAAECwxTYJRtrt7ffr7PhyzPeLXre0HnPKAECBAgQIECAAAECYy6gADrmJ8juESBAgAABAmsqsGvW3np6HtDZUhU9P5u0np43dt4zSoAAAQIECBAgQIDABAkogE7QybKrBAgQIECAwEAEdstaWk/P+3TWeFnGP5NU0fPoRNEzCBoBAgQIECBAgACBSRdQAJ30M2j/CRAgQIAAgX4E9shM65J6evu9OwtcmvFW9Dwm44qeHRyjBAgQIECAAAECBKZBQAF0Gs6iYyBAgAABAgTmE9gzE9vt7ft3Zrgk459O1idV9Lwp0QgQIECAAAECBAgQmFIBBdApPbEOiwABAgQIzKjAXjnuVvTcr2Nwccar6Fm3tx+bKHoGQSNAgAABAgQIECAwCwIKoLNwlh0jAQIECBCYboF9cnit6FnjrV2UkW7R8+b2hiEBAgQIECBAgAABArMjoAA6O+fakRIgQIAAgWkS2DcH04qee3cO7MKMH59UT88aKnoGQSNAgAABAgQIECAwywIKoLN89h07AQIECBCYLIG6pb0VPetW99YuyEi36HlLe8OQAAECBAgQIECAAAECCqD+HyBAgAABAgTGWaCe2F5Fzxck9VCj1s7PSCt61m3uip5NxpAAAQIECBAgQIAAgdsJKIDejsMLAgQIECBAYAwE7pN9aD09d+/sz3kZPy6p29s/myh6BkEjQIAAAQIECBAgQGBxAQXQxX28S4AAAQIECAxH4IBsZl1yRLJb0tq5GekWPW9tbxgSIECAAAECBAgQIECgHwEF0H6UzEOAAAECBAishcD9stJ2e/uunQ2ck/Fjk/XJCYmiZxA0AgQIECBAgAABAgRWJqAAujI3SxEgQIAAAQIrE7h/FmtFz3t1VvHzjFfRs25v/3yi6BkEjQABAgQIECBAgACB1QsogK7e0BoIECBAgACBxQUekLer6Hl4sktn1rMz3oqeX8i4omcHxygBAgQIECBAgAABAoMRUAAdjKO1ECBAgAABAr8S2CCj3aLnPX/11n84K+OfSqqn5xc7040SIECAAAECBAgQIEBgTQQUQNeE1UoJECBAgMDMCVTR84FJ6+l5j47AzzLeip4ndqYbJUCAAAECBAgQIECAwJoLKICuObENECBAgACBqRWooueDkyp6Pj/ZOWntpxlpRc+T2kRDAgQIECBAgAABAgQIDFtAAXTY4rZHgAABAgQmW2DD7H636LlT53DOzPgxSd3efnKiESBAgAABAgQIECBAYOQCCqAjPwV2YIwEtsq+HJrsn2yTXJB8M6kHc1yfaAQIEJhVgSp6PiRZl1RPzx2T1n6SkdbT85Q20ZAAAQIECBAgQIAAAQIECMyqwDdy4PWU36PGCKCKnX+VVJGz9m1uLs60VycbJxoBAgRmRaCKng9P3pqcl3SvjWfn9V8mj0w0AgQIECBAgAABAgTWTuDIrLo+ix++dpuY/jXrATr959gRLi6wX96unkt7Jjcnn0/qts1Lk7qt85CkHurx5uSw5FlJvacRIEBgGgU2ykE9NKnv9Pz1ZPuktSp61q3t9QHstDbRkAABAgQIECBAgAABAgQIELi9wDj1AK1f7OshHfWXlFOT+yTztSdmYv3iX/N9MdETNAgaAQJTI1BFz0clb0vqqz/qWtdST29/S3JgohEgQIAAAQIECBAgMHyB6oBQn8/1AB2+vS0SWLHAOBVAP5KjqIvIyclmSxzRPfL+WUnN/5ol5vU2AQIExl2gip6PTt6eXJi0gmcNz0zenNwv0QgQIECAAAECBAgQGK2AAuho/W2dwIoExqUAeu/s/S3J1UkVN/tpT8hMVRy4JNm0nwXMQ4AAgTESqK+9eUzy18lFSbfoeUZe/0VyQKIRIECAAAECBAgQIDA+AgqgAzgX9cuQRmAWBepJxhskdSH5eZ8An8t8/5I8OHl8clyiESBAYJwF6t/5ur29vtPzecm2SWv19Pb1yfuTf2sTDQkQIECAAAECBAgQIDBtAgqg03ZGHU+/AvVgo2on/HLQ939r/iqAPihRAO2bzYwECAxRoL6nuFv03Kaz7R9nvD3I6Lud6UYJECBAgAABAgQIECAwtQIKoFN7ah3YEgL1AKRq5/xy0Pd/z+3NuV3fS5iRAAECay9QRc+6vb16t1dPz62T1n6UkVb0/F6baEiAAAECBAgQIECAAIFZEVAAnZUz7TjnClzam9DtGTV3nvlet/kvm+9N0wgQIDBEgU2yrSp61u3tz0m6Rc8f5HUVPT+QfD/RCBAgQIAAAQIECBAgMLMCCqAze+pn/sCrIPCUpG4TXc6t7I/syelF1YMwIEBgqAJV9DwoaUXPrTpb//eMt56eVQDVCBAgQIAAAQIECBAgQIAAgREIjMtT4KvXVD0BuW5p37xPh/0z303JDUnrCdrnomYjQIDAigU2zZJPSt6bXJ50n95ef4z5s2TvRCNAgAABAgQIECBAYPoEPAV++s6pI5oBgXEpgBb1l5MqJFRRYalWBYh/Tmr+v15qZu8TIEBglQJ1zTk0+bvkiqRb9Kwntr8u2SvRCBAgQIAAAQIECBCYbgEF0Ok+v45uSgXGqQB6vxhflbQi6EI9QXfKPCf15vtJhtsmGgECBAYtsFlW+OTk/yVzi57fybQ/TfZMNAIECBAgQIAAAQIEZkdAAXR2zrUjnSKBcSqAFuthydVJFUHrifBvTKoA8bDkmck7k1YkPSvj9040AgQIDErgzllRXYfel1yZdHt6np7Xf5LsnmgECBAgQIAAAQIECMymgALobJ53Rz3hAuNWAC3O+ydfSbqFh7nj/5T3d0w0AgQIrFagip5PTf4haX9gadecb2faHyW7JRoBAgQIECBAgAABAgQUQAfw/4CnwA8A0SomXqAKDo9IDkqekeyfbJ1cmHwzWZ/U7acaAQIEVipwlyz4hGRd8uykXrdW16D6I8sHkp+2iYYECBAgQIAAAQIECBAgMBgBBdDBOFrLdAiclMOoaAQIEBiEwOZZSRU9/1NSX6nRLXqeltdV9Pxg8rNEI0CAAAECBAgQIECAAIE1ElAAXSNYqyVAgACBmRSooucTk1b0rNvdq9Ut7tWjvBU96zuFNQIECBAgQIAAAQIECBAYgoAC6BCQbYIAAQIEplrgrjm6Q5IqetbXaHSLnvW9x63oeXbGNQIECBAgQIAAAQIECBAYsoAC6JDBbY4AAQIEpkJgixxFt+i5We+oqqfn15Mqen4o+XmiESBAgAABAgQIECBAgMAIBRRAR4hv0wQIECAwUQJV9HxS0np6btrb+yp6npq0ouc5vekGBAgQIECAAAECBAgQIDAGAgqgY3AS7AIBAgQIjK3AltmzQ5Mqej4taUXPWzL+z8n6pHp6nptoBAgQIECAAAECBAgQIDCGAgqgY3hS7BIBAgQIjFRgq2y9W/TcpLc3VfT8alI9PT+cnJdoBAgQIECAAAECBAgQIDDmAgqgY36C7B4BAgQIDEVg62zlycm65KlJt+j5lbxuRc/zM64RIECAAAECBAgQIECAwAQJKIBO0MmyqwQIECAwUIFtsrYqetbt7YclGyfVbk5OSaro+ZHkgkQjQIAAAQIECBAgQIAAgQkVUACd0BNntwkQIEBgRQLbZqlW9HxKxrtFz5PzuhU9L1zR2i1EgAABAgQIECBAgAABAmMnoAA6dqfEDhEgQIDAgAWq6Fk9PKunZxU/2799N2X8S0krel6UcY0AAQIECBAgQIAAAQIEpkyg/RI4ZYflcAgQIEBgxgXuluNvRc96oFH7966KnicmVfT8x+TiRCNAgAABAgQIECBAgACBKRZovxBO8SE6NAIECBCYEYG75zi7Rc+NesddRc8vJq3oeUlvugEBAgQIECBAgAABAgQIzICAAuj4nuT6xf3Rvd37aYZnjO+u2jMCBAiMTGC7bLme2l63tx+StKLnjRk/MVmfVE/PSxONAAECBAgQIECAAAECBGZQQAF0fE/6XbNr1WOp2huTP/rFmP8QIECAwPYhaEXPJ2a8W/RsPT0/mumXoSJAgAABAgQIECBAgAABAgqg/h8gQIAAgUkQ2CE7+bRkXVJFzw2TajckX0jq9vaKomcQNAIECBAgQIAAAQIECBD4lYAC6K8s1mpsr6x4Jc5bdHaoHuaxX+d1G/1+GzEkQIDAFArsmGOqomfd3v74pFv0bD096xb3yxONAAECBAgQIECAAAECBAgQGJHAudnurWuUER3Sqjb7jZ7FUatai4UJEJhWgZ1yYC9JTkhuTtr187qMH5/8l2TLRCNAgAABAgQIECBAgMAsCByZg6zfiw6fhYNdq2NcSc/EtdoX6yVAgACB2RTYOYf99KR6ej422SCpVkXPbk/PK38x1X8IECBAgAABAgQIECBAgMAyBBRAl4G1wllfn+XekmzWW75+gT8uqer9Ym2TvPms3gzfzfD0xWb2HgECBCZM4B7Z31b0PDjj3aLn5/O6vs+zeooregZBI0CAAAECBAgQIECAAAEC4y5w7+zgaUm7lfPTGa8eT4u1rfJmm/8Ni804Ye+5BX7CTpjdJTBAgXtmXa9IqlfnLUm7xl2T8WOSI5K7JhoBAgQIECBAgAABAgQI/FLALfD+T5gogerR+RdJ+067izP+nEWOQAF0ERxvESAwMQK7ZE9/IzkpmVv0/GSmvSDZPNEIECBAgAABAgQIECBA4I4CCqB3NDFlAgQOzj7+LGk9nz6Q8Sp2zm0KoHNFvCZAYFIE7pUd/c3kS0m71tXw6uQTyfOTuyQaAQIECBAgQIAAAQIECCwuoAC6uI93x1hg6+zbh5JWGKiC6OPm7K8C6BwQLwkQGGuB3bJ3v5WcnLRrWw2vSj6e/Hqi6BkEjQABAgQIECBAgAABAssQUABdBpZZx1OgekFdllSRoG4NfWvSHpakABoMjQCBsRbYPXv328mXk7lFz49l2vOSOycaAQIECBAgQIAAAQIECKxMQAF0ZW6WGjOBulW0vhuvFQ++k/EHJAqgQdAIEBg7gT2yR7+TfCVp160a1tPa1yfPTRQ9g6ARIECAAAECBAgQIEBgAAIKoANAvNMA1mEVqxOo298fm7w2+bPkPsnXkrckGgECBMZBYM/sxK8l/yl5aGeHquj5meSfkqOT6xKNAAECBAgQIECAAAECBAgQILCgwAPzzveSbq+qGn/DgktM3hvf6B3fUZO36/aYwEwJ7JWjfXVSf5DpXpMuz+t/TNYlmyYaAQIECBAgQIAAAQIECKydgB6gA7DVA3QAiANcxTezriqCvjl55QDXa1UECBDoR6C+07MKm9XT8z92Frgi48cn1dPzU8n1iUaAAAECBAgQIECAAAECBCZCQAF0/E7Ttdml30iOTZ7R271Te0MDAgQIDFqgvtOzCp71lPb7dVZePT2PS+p7PavoeUOiESBAgAABAgQIECBAgACBiRNQAB3fU1a9rSoaAQIEBi1Q3+nZip4HdFZ+Wcar6Fk9PWuo6BkEjQABAgQIECBAgAABAgQmW0ABdLLPn70nQIBAvwJ7Z8Yqev7n5L6dhS7NeLfoeWPnPaMECBAgQIAAAQIECBAgQGDiBRRAJ+sUbpzd3aGzy2d3xo0SIEBgrsA+mdB6et678+YlGT82qZ6en04UPYOgESBAgAABAgQIECBAgMB0CiiATtZ5re/n+5fOLm/QGV/L0Sdl5S9INhzARnbrrWOzAazLKggQuKPAvpnUip77d96+OOPdoudNnfeMEiBAgAABAgQIECBAgACBqRVQAJ3aUzvQA3t51tYeyDSoFW83qBVZDwEC/6EKnVX0rNvb9+t4VNGzHmBUPT0/kyh6BkEjQIAAAQIECBAgQIAAgdkSUACdrfO90qN9WRb8SDKIHqdvzHp2T9y+HwSNwCoE6pb21tOzbnVv7aKMHJNU0fOERNEzCBoBAgQIECBAgAABAgQIECAwGQJVsK7vAG2ZjL2+/V5+Iy9vTY66/WSvCBDoQ6AeXvS65AdJ/Ry1XJDxv0sOTTZKNAIECBAgQIAAAQIECBCYDoEjcxj1u9/h03E4ozkKPUBH477SrVZPrvNXurDlCBCYSIEDstft9va9OkdQRc+jk/XJ55KbE40AAQIECBAgQIAAAQIECBCYI6AAOgfESwIECIyBQD3wrBU99+zsT/0BpIqedXv755NbEo0AAQIECBAgQIAAAQIECBBYREABdBEcbxEgQGCIAgdmW1X0fF6yR2e752W8FT2/kHFFzw6OUQIECBAgQIAAAQIECBAgsJSAAuhSQmv//s7ZxLbJXXq5LsPLkyuSeoJzvdYIEJhOgQfksFpPz906h3huxj+ZVE/PExNFzyBoBAgQIECAAAECBAgQIEBgJQIKoCtRW90yW2TxI5LnJ/VAk3q9UKvv/PzX5GvJp5LjkvriW40AgckVeGB2vRU9d+0cxjkZ7xY9/ax3cIwSIECAAAECBAgQIECAAAEC4y9QT25/R1I9O6uwsZJUMfSwZJLbN7LzdeyeAj/JZ9G+L0dgg8z84OT/JD9Nuj/7Z+d1XRcOTmo+jQABAgQIECBAgAABAgQIdAU8Bb6rscJxPUBXCLfMxbbJ/CckB3SWqyJI3eb6s+TC5Nrk+qTOyWbJlskuya7Jpkm16jF6dPI/kr9KNAIExlOgFT2rp2d9p2f9LLdWRc9PJHV7+8lJXQs0AgQIECBAgAABAgQIECBAgMDECmyePf9K0np9nZrxKohsl/TTNs5Mj0zendyQtPU8JeOT2PQAncSzZp/7Eaii50OTNydnJe1ntYb1h463J49O9PQMgkaAAAECBAgQIECAAAECfQnoAdoXk5lGLfDi7EArhHw44xuuYoeq6NmKoKevcl2r2I1VLaoAuio+C4+ZQBUzH5a8Jamene1nvYZnJtVT+1GJRoAAAQIECBAgQIAAAQIEViKgALoSNcsMXeBvs8Uqhnw7qd6cq22vygpakWXP1a5sBMsrgI4A3SYHKlB/xHh48tbk50n7eazhGclfJo9INAIECBAgQIAAAQIECBAgsFoBBdDVCmZ53wE6AMQlVlG3r1c7JrnxF2Or+8/HsvjbeqvYJ8Mfr251liZAoA+BVvSs7/R8TrJTZ5kqerbv9PxqZ7pRAgQIECBAgAABAgQIECBAYAwEFEDX/iTcs7eJswa0qYuzniqkVm/SOw9onVZDgMAdBaroWT05W9Fzx84sP8n4x5N6kNHXOtONEiBAgAABAgQIECBAgAABAmMmoAC69iekemgemNQts/Ugo9W2Ksi0W+lPW+3KLE+AwO0ENsqrbtFzh8679bPcip71MDONAAECBAgQIECAAAECBAgQmAABBdC1P0n1nZdVAH1u8vfJSclK29ZZ8C29hS/JsG691QgQWJ1AFT3rQUXV07OyfdLajzLSip5fbxMNCRAgQIAAgTUTqN9PHprsnmySnJPUV8xcnmgECBAgQIAAAQJjKrBn9uuG5NbksuSlSX2YW26rImr1Oqv1VN6YTGKrgnDt/1GTuPP2eWoEquh5cPKO5IKk/VzV8N+TP08elGgECBAgQIDAcATqD/3/J6k/8nf/Xa7x+iy9Ptkv0QgQIECAwKwJHJkDrn8PD5+1Ax/k8eoBOkjN+ddVt83+QfLmZKvkXb3x6gn6reSM5Pzk2uS6pM7JZsmWyS7JXsljkvsmrX02I3/cXhgSINCXQP1s1c/SuqR6et49aa1+Tuv7PCvfbBMNCRAgQIAAgaEIPCBb+WRSn32rfSf5dnJ9Up0J6qGiz06elrw8+X+JRoAAAQIECBAgMIYCL84+XZPM/Yv2cl8fn3VsO4bH1+8u6QHar5T5BiFQRc/HJ/WHh4uS7s/bD/K6elIfkGgECBAgQIDAaAT2zWYvTerf6C8nD0zmtvp6mvou/fbv+BFzZ/CaAAECBAhMsYAeoFN8cqf10LbLgVXB5dykfYDrZ1g9Qz+RPDWZ9KYAOulncPz3f+Ps4hOS+kXp4qT7M1a3t78h6faozkuNAAECBAgQGIHAhtlm3RFV/1avT+rf8MXaK/JmzVufjes7QjUCBAgQIDALAgqgAzjL1TtKG57AhdnUH/ayW4YPS/ZO6nb3uj1+i+TG5KrkiqRuy/1uUrcA1TSNAIH5BeoXpscmdWt73SK3TdJaFT3r1vYPJ/XzpBEgQIAAAQLjIVAPCb1/ckZSvTrrc/Bi7Z15sx6QVPO+LnlhohEgQIAAAQIECBAYOwE9QMfulEzsDtXDxJ6UvDeZ+8CEKnT+r2T/RCNAgAABAgTGU+CY7Fb16HzJMnZv18x7S3JlsukyljMrAQIECBCYVAE9QAdw5vQAHQCiVRAgMDSBKno+Lqmens9K6omxrVXRs3p6fiT5fptoSIAAAQIECIytQD3cqNrRvxz09d+fZq5/Te7Xy9f7WspMBAgQIECAwEwLKIDO9Ol38AQmQqB6d9SDjKro+cykvi6itXpKbH1nWN3eXg810ggQIECAAIHJEKh/3+sra65PzlvmLp+Z+asAutMylzM7AQIECBAgMKMCCqAzeuIdNoExF6hfip6QtKJnfU9ua9Xro/X0/GGbaEiAAAECBAhMlMAN2dv6zs+6u6O+y3up7//MLLe1u/TGrrltihECBAgQIECAwCICCqCL4HiLAIGhCmyWrT0xWZdUT896KFhrp2ekFT1/1CYaEiBAgAABAhMrUN/9eWZSDwR9QHJq0k/bKDMd2JuxHhiqESBAgAABAgSWFFAAXZLIDAQIrKFAFT0PSaqn5zOSbtHzW3ldRc9/TPyCEwSNAAECBAhMmcCxOZ7fTv5r0m8BtD4v3D2p7/s+I9EIECBAgAABAgQIjJ2Ap8CP3SkZ+g7dOVusX14+kNQTXKsHSMs3M/77yR6JRoAAAQIECEy3QPX+rFvfK4/q41C3zTw/Sepzw8v6mN8sBAgQIEBgGgQ8BX4azqJjmDkBBdCZO+W/OOD6rq66rf1DyVVJK3jWsP6f+J/JbolGgAABAgQIzJbAm3K49Xng4uSgRQ5957xXvURr3hq6ky0IGgECBAjMhIAC6EycZgc5bQIKoNN2Rhc+nip6PiupJ7TPLXp+PdNem+yaaAQIECBAgMDsCmyYQ1+fVGHz5qTuEKnvBN8+2Sp5UPKG5PKk5qnvAq9iqEaAAAECBGZFQAF0Vs6045wqAQXQqTqddziYzTPl2clHkquT+kWlcktSvTVek9wr0QgQIECAAAECTaCKoK9LrkvaZ4f5hh/P+3UbvEaAAAECBGZJQAF0ls62Y50aAQXQqTmVtx3IXTNWDzH6aHJN0n5hqaLnPyevTnZJNAIECBAgQIDAYgL1R9LXJV9Lzk8uS/4t+ZvkEYlGgAABAgRmUUABdBbPumOeeAEF0Ik/hb84gCp6Piepp7TPLXp+NdN+N7lnohEgQIAAAQIECBAgQIAAAQIrF1AAXbndbUve6bYxIwQIEFhcYIu8fViyrjeg8LFVAAA2V0lEQVTcrDd79fisomcVQ6sX6M8TjQABAgQIECBAgAABAgQIECAwFgIKoGNxGuwEgbEV2DJ7VkXPusX9KcmmSbW6vf3LSRU9K+ckGgECBAgQIECAAAECBAgQIEBg7AQUQMfulNghAiMXqCeutqLnkzPeLXqektet6HnuyPfUDhAgQIAAAQIECBAgQIAAAQIElhBQAF0CyNsEZkSgip5PS6qn56HJJkm16ul5ctKKnufVRI0AAQIECBAgQIAAAQIECBAgMCkCCqCTcqbsJ4HBC2ydVbai55My3oqeN2f8pKSKnuuTegqrRoAAAQIECBAgQIAAAQIECBCYSAEF0Ik8bXaawIoFtsmS3aLnxr01VdHzxKQVPS/oTTcgQIAAAQIECBAgQIAAAQIECEy0gALoRJ8+O0+gL4FtM9fTk7q9/YlJt+j5hbyuXp6VCxONAAECBAgQIECAAAECBAgQIDBVAgqgU3U6HQyB2wTulrFu0bP9rN+U6Z9Pqqfnx5KLEo0AAQIECBAgQIAAAQIECBAgMLUCrSgytQfowAjMkMDdc6zPSNYlT0jaz3cVPT+XtKLnxRnXCBAgQIAAAQIECBAgQIAAAQIzIdAKJDNxsA6SwBQKbJdjqqJn3d7+uKT9TN+Y8c8mVfQ8Krkk0QgQIECAAAECBAgQIECAAAECMyfQiiUzd+AOmMAEC1TR89eSVvTcqHcsVfT8TNKKnpf2phsQIECAAAECBAgQIECAAAECBGZWQAF0Zk+9A58wge2zv89Mquh5cNKKnjdk/ISkip4fTxQ9g6ARIECAAAECBAgQIECAAAECBJqAAmiTMCQwfgI7ZJe6Rc8Ne7tYRc/W0/MTGb+sN92AAAECBAgQIECAAAECBAgQIEBgjoAC6BwQLwmMWGDHbL8VPQ/KeCt6Xp/x9iCjKnpenmgECBAgQIAAAQIECBAgQIAAAQJLCCiALgHkbQJDENgp23hWUre3PzrpFj3rQUbrkyp6XpFoBAgQIECAAAECBAgQIECAAAECyxBQAF0GllkJDFBg56yrFT0flfFW9Lwu41X0rO/0/GRyZaIRIECAAAECBAgQIECAAAECBAisUEABdIVwFiOwAoF7ZJlnJ+uSKnpukFSromf7Ts+jM67oWSoaAQIECBAgQIAAAQIECBAgQGAAAgqgA0C0CgKLCOyS91pPz0dkvBU9r834p5Pq6XlMclWiESBAgAABAgQIECBAgAABAgQIDFhAAXTAoFZHIAL3SlrR8+EZb0XPazLeLXpendcaAQIECBAgQIAAAQIECBAgQIDAGgoogK4hrlXPlMCuOdq6vb0eZPTQpFv0PD6vq6fnpxJFzyBoBAgQIECAAAECBAgQIECAAIFhCSiADkvadqZRYLccVLfo2Y6xipzHJVX0PDapnp8aAQIECBAgQIAAAQIECBAgQIDACAQUQEeAbpMTLbB79r4VPR/SOZL6Ds9u0bO+41MjQIAAAQIECBAgQIAAAQIECBAYsYAC6IhPgM1PhMAe2ct6cnvd3v7gzh5X0fNTyfqkip+KnkHQCBAgQIAAAQIECBAgQIAAAQLjJKAAOk5nw76Mk8Ce2ZlW9HxQZ8euzHgVPev29vpuz+sSjQABAgQIECBAgAABAgQIECBAYEwFFEDH9MTYrZEI7J2tVtGz8sDOHlyR8W7R8/rOe0YJECBAgAABAgQIECBAgAABAgTGWEABdIxPjl0bisA+2UoVPOv29gM7W7w848ck1dPzM4miZxA0AgQIECBAgAABAgQIECBAgMCkCSiATtoZs7+DENg3K2lFz/t3VlhFz6OTVvS8ofOeUQIECBAgQIAAAQIECBAgQIAAgQkUUACdwJNml1cksF+Wql6elQM6a7gs463o+dmMK3p2cIwSIECAAAECBAgQIECAAAECBCZdQAF00s+g/V9MYP+82Yqe9+3MeGnGP5lUT88TkhsTjQABAgQIECBAgAABAgQIECBAYAoFFECn8KTO+CHdJ8dft7c/J7l3x+KSjLei5+cyrujZwTFKgAABAgQIECBAgAABAgQIEJhWAQXQaT2zs3Vc1buz9fSsXp+tXZyRTyTrkyp63pRoBAgQIECAAAECBAgQIECAAAECMySgADpDJ3vKDrW+x7MVPev7PVu7KCNV9Kzb27+QKHoGQSNAgAABAgQIECBAgAABAgQIzKqAAuisnvnJPO56Ynsreu7TOYQLM96Knl/MuKJnB8coAQIECBAgQIAAAQIECBAgQGCWBRRAZ/nsT8axH5jdbEXPvTu7fEHGP55UT88Tk5sTjQABAgQIECBAgAABAgQIECBAgMDtBBRAb8fhxZgIPCD70Yqee3X26fyMt6LnSRlX9OzgGCVAgAABAgQIECBAgAABAgQIELijgALoHU1MGY3Ag7LZKnrWE9z37OxCFT2PSqqnZxU9b0k0AgQIECBAgAABAgQIECBAgAABAn0JKID2xWSmNRJ4cNbbenru3tnGeRn/WFJFz5MTRc8gaAQIECBAgAABAgQIECBAgAABAssXUABdvpklBiNwSFbzzM6qzsl46+l5SsYVPTs4RgkQIECAAAECBAgQIECAAAECBFYmoAC6MjdLrV5g86zi50n19FyffDlR9AyCRoAAAQIECBAgQIAAAQIECBAgMDgBBdDBWVrT8gTq+zwfm9y6vMXMTYAAAQIECBAgQIAAAQIECBAgQKB/gQ37n9WcBAYqcEnWpvg5UFIrI0CAAAECBAgQIECAAAECBAgQmCugADpXxGsCBAgQIECAAAECBAgQIECAAAECBKZGQAF0ak6lAyFAgAABAgQIECBAgAABAgQIECBAYK6AAuhcEa8JECBAgAABAgQIECBAgAABAgQIEJgaAQXQqTmVDoQAAQIECBAgQIAAAQIECBAgQIAAgbkCCqBzRbwmQIAAAQIECBAgQIAAAQIECBAgQGBqBBRAp+ZUOhACBAgQIECAAAECBAgQIECAAAECBOYKKIDOFfGaAAECBAgQIECAAAECBAgQIECAAIGpEVAAnZpT6UAIECBAgAABAgQIECBAgAABAgQIEJgroAA6V8RrAgQIECBAgAABAgQIECBAgAABAgSmRkABdGpOpQMhQIAAAQIECBAgQIAAAQIECBAgQGCugALoXBGvCRAgQIAAAQIECBAgQIAAAQIECBCYGgEF0Kk5lQ6EAAECBAgQIECAAAECBAgQIECAAIG5Agqgc0W8JkCAAAECBAgQIECAAAECBAgQIEBgagQUQKfmVDoQAgQIECBAgAABAgQIECBAgAABAgTmCiiAzhXxmgABAgQIECBAgAABAgQIECBAgACBqRFQAJ2aU+lACBAgQIAAAQIECBAgQIAAAQIECBCYK6AAOlfEawIECBAgQIAAAQIECBAgQIAAAQIEpkZAAXRqTqUDIUCAAAECBAgQIECAAAECBAgQIEBgroAC6FwRrwkQIECAAAECBAgQIECAAAECBAgQmBoBBdCpOZUOhAABAgQIECBAgAABAgQIECBAgACBuQIKoHNFvCZAgAABAgQIECBAgAABAgQIECBAYGoEFECn5lQ6EAIECBAgQIAAAQIECBAgQIAAAQIE5googM4V8ZoAAQIECBAgQIAAAQIECBAgQIAAgakRUACdmlPpQAgQIECAAAECBAgQIECAAAECBAgQmCugADpXxGsCBAgQIECAAAECBAgQIECAAAECBKZGQAF0ak6lAyFAgAABAgQIECBAgAABAgQIECBAYK6AAuhcEa8JECBAgAABAgQIECBAgAABAgQIEJgagTtNzZFM3oFsml2+fgW7fbcsc+fecmevYHmLECBAgAABAgQIECBAgAABAgQIEJgZAT1Ah3uq12VzxyfnJ9cm30venzwy6be9LzOe1Uu/y5iPAAECBAgQIECAAAECBAgQIECAwEwKKIAO57Rvns38Q/JPyaHJ9skGyX7JC5IvJW9NWs/OjGoECBAgQIAAAQIECBAgQIAAAQIECKxWQAF0tYL9Lf+mzHZEZ9arM35GcmtvWp2H30m+lezem2ZAgAABAgQIECBAgAABAgQIECBAgMAqBRRAVwnYx+IHZp5X9uarW9+fkWyZ7JFsk7w2uTyptk9yYqIIGgSNAAECBAgQIECAAAECBAgQIECAwGoFFEBXK7j08i/PLBslNyVPSo5ObkmqVeHzzcn+ybeTavdKPp/sUC80AgQIECBAgAABAgQIECBAgAABAgRWLqAAunK7fpes4ma1DyWtyPmLCZ3/nJvxxyQn9aZVD9Bjk/ruUI0AAQIECBAgQIAAAQIECBAgQIAAgRUKKICuEG4Zi+3bm/cbSyxzRd5/cvLV3nwPyvCjSfUe1QgQIECAAAECBAgQIECAAAECBAgQWIGAAugK0Ja5yCa9+a/pY7lrM8/Tkx/15n1Khn/dGzcgQIAAAQIECBAgQIAAAQIECBAgQGCZAgqgywRbwew/7C1z7z6XvSjzHZpc2Ju/vkP0d3vjBgQIECBAgAABAgQIECBAgAABAgQILENAAXQZWCuctRVAn5/lt+1zHT/OfNUTtHqEVvv/kiN+MeY/BAgQIECAAAECBAgQIECAAAECBAj0LaAA2jfVimeshx9V2z6p8X6f7v7PmbeKpvXE+A2Sv0/+NHHOgqARIECAAAECBAgQIECAAAECBAgQIDA+AidkV27t5ZIMq5j5G0k/7aWZqYqgbfmbO+P9LD9u89TDoOpYjhq3HbM/BAgQIECAAAECBAgQIECAAIExEzgy+1N1lMPHbL/sDoE7COyRKacnrYhZw+/cYa6FJ7wob92YdJev8UlsCqCTeNbsMwECBAgQIECAAAECBAgQIDAKAQXQAai7nXoAiH2s4ieZ5yHJO5Kre/Of0xv2M3hfZnpAcnI/M5uHAAECBAgQIECAAAECBAgQIECAAIFfCiiADu//hOuyqbrtfevk4Uk92Gg5rXqMPiZ5YVLfD3pFohEgQIAAAQIECBAgQIAAAQIECBAgsIjAnRZ5z1trI3BTVlsFzJW292fBikaAAAECBAgQIECAAAECBAgQIECAwBICeoAuAeRtAgQIECBAgAABAgQIECBAgAABAgQmV0AP0Mk6dxtnd3fo7PLZnXGjBAgQIECAAAECBAgQIECAAAECBAjMEVAAnQMy5i/vl/37l84+btAZX8vRegDTs5NB9BjeubejVczVCBAgQIAAAQIECBAgQIAAAQIECKypgALomvJOzcpfnyM5bMBH0+3JOuBVWx0BAgQIECBAgAABAgQIECBAgACBXwoogPo/oR+B12amU5JB9Dh9Rtbz0OSTiUaAAAECBAgQIECAAAECBAgQIEBgTQUUQNeUd+Ar/3bWuOPA17r0Cr+bWSqDaNtnJVUAvXoQK7MOAgQIECBAgAABAgQIECBAgAABAosJKIAupjN+792UXTp//HbLHhEgQIAAAQIECBAgQIAAAQIECBAYTwEF0PE8L/aKAAECBNZeYNts4vHJvZL69/DnyRd7www0AgQIECBAgAABAgQIEJgGAQXQaTiLjoEAAQIEliOwR2Z+U7Iu2WjOgrfm9eeT30u+Oec9LwkQIECAAAECBAgQIEBgAgUUQEd/0nbOLlQvpLv0cl2GlydXJBcn9VojQIAAgcEIPDWr+VCyRXJD8rnkO0l9xcg+yROTJyRfS34reWeiESBAgAABAgQIECBAgAABAssQqF+6X5l8JakiZ/U2Wig35r3qgfQ3yWHJIJ7CntWMtP1ltl7H+9sj3QsbJ0BgFgUOykFX0bOuQR9J6g9Qc9tWmfDWpF2XXzR3Bq8JECBAgAABAgQIECAwRIEjs636/eTwIW7TpgisWGCHLPmOZKmiZ/ule77hv2b5KoROclMAneSzZ98JTK5A9bKv7/isa+ub+ziMl/TmvTbD+o5QjQABAgQIECBAgAABAqMQUAAdgLpb4AeA2Mcqtsk8JyQHdOatX8LPTX6WXJjUL9nXJ3VONku2THZJdk02TardNzk6+R/JXyUaAQIECPQn8PLMVj0+69b23+tjkfdknkcn9VfWP0qqIKoRIECAAAECBAgQIECAAAEC8whsnml1u3vr0Xlqxp+XbJf00zbOTI9M3p20WzdrXU9JJrHpATqJZ80+E5h8gbr21rXzacs4lH16y1yc4dyHJS1jNWYlQIAAAQIECBAgQIDAigX0AF0xnQWHKfDibKwVPz+c8Q1XsfEqerYi6OmrXNcqdmNViyqArorPwgQIrECgipc3J/Wgo9ajvt/V/Dgz1jV8334XMB8BAgQIECBAgAABAgQGKKAAOgDM1RTjBrD5mVjFI3pHWQXLI5JbVnHUx2XZV/eWr9vpd1/FuixKgACBWRGoHvf171193Uh91chy2lm9mXdczkLmJUCAAAECBAgQIECAAIHxEVAAXftzUbevVzsmqae6r7Z9rLOCuj1TI0CAAIHFBa7svb3F4rPN+259H3O1eoCdRoAAAQIECBAgQIAAAQITKKAAuvYn7Z69TbReRKvdYn0XXSuk3nm1K7M8AQIEZkDg6hzjOUl9J3M9TK7fVgXT+yR1+/xP+l3IfAQIECBAgAABAgQIECAwXgIKoGt/Pur746o9/JeDVf+3bqmvByNVO+2XA/8lQIAAgSUEqhd+tZf9ctDXf1+UuTZJTk4uTzQCBAgQIECAAAECBAgQIEBgHoH3Zlo9QOPa5KB53l/OpK0zcxU9a33VE3QSm4cgTeJZs88EJl9gvxxCPQSpetA/uo/D2TPzXJLU9fawPuY3CwECBAgQIECAAAECBNZC4MistH4vOXwtVm6dBAYlUL9Etye3X5bxlybVo2i57cAscGpS/9NX3phMYlMAncSzZp8JTIfAm3IYdf28NDl0kUOq6+2ZSc37sUQjQIAAAQIECBAgQIDAqAQUQAcgf6cBrMMqFheoW+D/IHlzslXyrt74SRl+KzkjOT+pHqLXJXVONkvqwRu7JHslj0m631v32bz+40QjQIAAgf4F/iiz7pb85+T45FPJB5LvJNU7dJ9kXfL8ZKPky8kRiUaAAAECBAgQIECAAAECBAj0IfDizHNNUj2KVpP6pX3bZFKbHqCTeubsN4HpENggh/GapJ7qvtC1uHrt17VqJb31s5hGgAABAgQIECBAgACBgQnoATowSisalsB22VDdun5ustAv3vNNr56hn0iemkx6UwCd9DNo/wlMh8D2OYzfSo5Lqgfo95PPJX+Y7J5oBAgQIECAAAECBAgQGAcBBdABnAW3wA8AcRmruDDz1i/Xld2ShyV7J3W7+1bJFsmNyVVJ9U6q2+e/m3w7qWkaAQIECAxG4IKs5m29DGaN1kKAAAECBAgQIECAAAECYymgADq603JmNl3RCBAgQIAAAQIECBAgQIAAAQIECBBYI4EN12i9VkuAAAECBAgQIECAAAECBAgQIECAAIGRCyiAjvwU2AECBAgQIECAAAECBAgQIECAAAECBNZKQAF0rWStlwABAgQIECBAgAABAgQIECBAgACBkQsogI78FNgBAgQIECBAgAABAgQIECBAgAABAgTWSkABdK1krZcAAQIECBAgQIAAAQIECBAgQIAAgZELKICO/BTYAQIECBAgQIAAAQIECBAgQIAAAQIE1kpAAXStZK2XAAECBAgQIECAAAECBAgQIECAAIGRCyiAjvwU2AECBAgQIECAAAECBAgQIECAAAECBNZKQAF0rWStlwABAgQIECBAgAABAgQIECBAgACBkQsogI78FNgBAgQIECBAgAABAgQIECBAgAABAgTWSkABdK1krZcAAQIECBAgQIAAAQIECBAgQIAAgZEL3Gnke2AHZlXg93PgL53Vgx/BcW+ebd4juTm5ZQTbt0kCBMZfYIPsYn0ucJ0Y/3NlDwmMSsB1YlTytktgcgTadeKC7PJlk7Pb9pTAWAvsPNZ7NyE7pwA6ISdqinbzzN6xbJ9hRRuugF7fw/W2NQKTKOA6MYlnzT4TGK6A68RwvW2NwCQK7JidrmgECAxG4Nas5qeDWdVsrqX+OqMRGLbAntngxsPe6Ixv7zk5/v+VHJf83xm3cPgECMwv8PRMflnyyeTd889iKgECMy7w7Bz/f00+lvzdjFs4fAIE5hd4bia/MHlX8rb5ZzGVAIEVCFyVZc5ewXIW6QnoAep/hVEI/HgUG53xbZ7fO/6zMjx+xi0cPgEC8wvs3Ztcf1l2nZjfyFQCsy5w3x7AGRm6Tsz6/w2On8D8Ag/sTb44w+/PP4upBAgQGL6A21eGb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBAgQIECAAAECBAgQIECAAAECBAgMSUABdEjQNkOAAAECBAgQIECAAAECBAgQIECAwPAFFECHb26LBEYhcEVvo5ePYuO2SYDARAi060QbTsRO20kCBIYq0D5HtOFQN25jBAhMhED7HOE6MRGny04SIECAAIHpEtgoh/PUZIvpOixHQ4DAAAXulHXVdWLzAa7TqggQmC6BjXM4T0vuMl2H5WgIEBigwCZZV10nNhvgOq2KAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBKZCYM8cxXuT05Irku/2Xr84w82TQbbDsrIPJqcmlybnJ19K3p0cmGgECIynwDCvE/MJvCITz+tlr/lmMI0AgZELDPM68aAc7Z8lxyX1WaJyUvLGZKtEI0BgPAWGdZ3YLIf/+8nxyRnJlck3k/o95HGJRoAAAQIECMyYwKtzvDckty6Qr2T6Nslq2x5ZwQnJQtup6Tclb0sGXXTNKjUCBFYhMKzrxEK7eO+8cW3Srh/7LTSj6QQIjExgmNeJ38xRLvbZ5YK8X39w1QgQGC+BYV0nDsph/zhpnxvmG34g7/tjyXj9/2FvCBAgQIDAmglUD8/2gaCKC+9LXpq8IflW0t47PeM7JCtt9RfYWkdbX/XSeGvy35JXJf+Q3Ji09+u1RoDAeAgM6zqx0NFukjeqd3q7PtRQAXQhLdMJjEZgWNeJDXJ470/a9eD6jB+bvCx5TVJ/tG3vVW+vfRONAIHxEBjWdWKXHG7dZdauBXXXWV0fDk/+PLksae/9Y8Y1AgQIECBAYMoFtsvxXZPUB4D6IHBQ0m0b58WHk/YB4R3dN5c5/n876/l0xredZ/n7Z9p5nfnWzTOPSQQIDFdgmNeJhY7sL/JGuw61oQLoQlqmExi+wDCvE/8lh9euA/+e8XvMOdwN87p7zfjSnPe9JEBgNALDvE7ULe/tOlG/v2w055B3zuufdOZ53pz3vSRAgAABAgSmTKC+I6t9OKhen/O1+kWi/mpa81VPii2S5bY7ZYGrklrHJcliPUmf3puv5q0PLxoBAqMVGNZ1YqGjPDhv3JzUNaG+n7iGFQXQIGgExkRgWNeJTXO8FyZ1Dbg6uVcyX6tiRxVHa766flThRSNAYLQCw7xOtK/H+FkOue4ima89ORPbZ4qPzDeDaQQIECBAgMD0CJybQ6l/+KuosNCHgzra+qto+4DwypqwzPawzN+W//sllq2CayuW1m3yGgECoxUY1nVivqPcOhPrl5e6flTP8foFpV1L9s24RoDAeAgM6zrxzBxuuwa8folDrwef/CCpW+IfucS83iZAYO0FhnWdqIejtevEYre33znz1bMHat4fJhoBAgQIECAwpQK75bjah4NjljjG6jlxS2/++kViue2QLPDZ5DvJb/SxcLslpba5aR/zm4UAgbUR2C2rHdZ1Yr4j+HBv+xdnWLertde1T/smGgECoxfYLbswrOvEhzrbqqdIawQITIbAbtnNYV0nugXQxe4mqweutjtMfjoZjPaSAAECBAgQWIlAt1fnUr0oav0/T+qDS/UWXctWT2JsxdbvreWGrJsAgSUFRnmdeH72rv2y9JzeniqALnnKzEBg6ALDvE6029oVK4Z+mm2QwKoEhnmduGv2tL4ioz5D1IOQ7p7M1+qzRfuc8cn5ZjCNAAECyxWo21k1AgTGT2Dvzi6d0RlfaLRuQ61W3wFaPbHWqr0kK64nvFar7x7VCBAYncCorhO75pDf0TvsD2b40dER2DIBAksIDOs6Uber7tXbl2/1hvV7xqOSP0g+nXw5eXtSxRa/gwRBIzAmAsO6TtTh1ldptc8Q9VU6RybbJN1WvUT/ujehOl68ufumcQIECKxUoB5+ohEgMH4CW3Z2qZ/v2qyHDrS2bUbOaS8GONwp6/rD3vrqw8h7BrhuqyJAYPkCo7hOVNHi/Un1Bj8r6edrMzKbRoDAiASGdZ2oP4y0omZ9LcbGSV0rqtjZbY/Ii99M/nvywuTsRCNAYLQCw7pOtKOsP4rU7xWHJ4cm1Xv8hKR+f9k/qWkbJTckL01OSTQCBAisWkABdNWEVkBgTQSquNDatW1kkWF3nrssMt9K36r9qe/pafv1toxXTw6NAIHRCbSfx9qD7jVgoT3qzrPS68RrsvLHJLcmL0ouSzQCBMZXYFjXiboDpbXrMnJ0UkWMeojJd5N6iEn1Mrt3Ur9/PC45LTkgOS/RCBAYncCwrhPtCOu68ILkpOTdyXbJryfddkFePD6pZxRoBAgQGIhA+0vtQFZmJQQIDExg7i8SS634+s4MKy1sdFZxu9G6ra2+e+f+vak/yLD1BO1NMiBAYAQCw75OPDDH+PrecdYfQb4wgmO2SQIElicwrOtEdzvVu7OKn1XgrM8OlXW94QMybAWNu2f8rxKNAIHRCnR/fusPGEu11f7esU02UH8keU/S6hH1B9X6HaMefFRt+6QKpK+oFxoBAgQGIdAuOINYl3UQIDA4gRs7q+qnp3Z3nn4+uHRWv+ho/XLy+eSg3lw/y7B+qen2JOu9ZUCAwJAFhnmdqD+EfDDZOKneXL+faAQIjL/AsK4Tm3Qo6jPJz5P67FDXi26r4udjk9Z7/LkZr17lGgECoxMY1nWijnCr5EvJ05J6rsApyQFJFUX3Terp7/X1GJck9bVe9X2hPnMEQSNAYPUCCqCrN7QGAmshcFVnpZt1xhca7c5z+UIzLXP6Xpn/q8nDe8udkeHBSQ01AgRGLzDM60Q9gGC/pH5Jqu/sGuQfWrI6jQCBNRIY1nWiu506lN9LrlzgmC7K9P/deU8BtINhlMAIBLo/v93fKRbale48y/2943ez0vv2VnxChvWHku/0Xtegepe+P3lI0var7j7ZO9EIECCwKgEF0FXxWZjAmglc0Vlz94vJO5NvN9qdp7vs7WZaxouHZd6vJFUErfaNpAqhip+loREYD4Huz3r3GrDQ3nXn6S670Pxt+pMz8srei7dkWNeBredJtwdYbavNU73BNAIERiPQ/VnvXgMW2pvuPN1lF5q/TZ9b7PxSe2OB4Zc70+t7QTUCBEYn0P1Z714DFtqj7jzdZReavzu9fZ64JRP/e1LD+dqPM/FPem9slOFvzTeTaQQIEFiOgALocrTMS2B4AvWPfmu7tJFFhm2e+lLxixeZr5+3npmZvpDUF5JXOy6pv86eXy80AgTGRmBY14mnd474f2b80gXyrM58p3bmeWRnulECBIYrMKzrxNmdw6qe4t3XnbduG/3RbWO/+mNrZ5JRAgSGKDCs60T9bnG33nHVNeCnSxzjpzvv123yGgECBFYloAC6Kj4LE1gzge53ZrVemAttbOO8sWvvzX/NcDW3pr40y69P6vv+qv1NUsWPq+uFRoDAWAmM6joxVgh2hgCBRQWGdZ2oP76e29uT+lyy56J79cvv+2uz1B9VNAIERicwrOtEK37WkZ7Tx+H+pDPPDp1xowQIEFiRgNvSVsRmIQJrLvDtbKG+A2fT5DFLbO0hvflqtq8tMe9ib78ob1bBs76Q/Nbk1clbE40AgfEUGNZ14vgcfn1n31KteoC2W1nflfG2zFI9PJZar/cJEFi5wLCuE7WH9Rnk13q7Wl+b0+3l2Zt822Dv28Z8vU6HwiiBkQgM6zpR14T2+82DMl63tt+8yBF3/5Dy/UXm8xYBAgQIECAw4QKfyP5XIbLygEWO5d2d+Q5bZL7F3qovI69b1mpb9UHkiEQjQGD8BYZ5nVhK48OZoV2z9l1qZu8TIDA0gWFdJ56TI2rXgGMzXn9QXagdlTfavE9eaCbTCRAYmsCwrhPfyBG1n/2lviLntZ15/3RoEjZEgAABAgQIDF3gqdli+4BQ36e39Tx78JRMu6E3X93+Pt8vG9XT+8Gd1K1pc1s9rKBt60/mvuk1AQJjKzDM68RSCAqgSwl5n8BoBIZ1nagnQ5+ZtM8T/3uBw+3uT/UQr15gGgECoxXo/lyu5e8d9RCkdo04K+O7L3DYdUfJNb15r81wvwXmM5kAAQIECBCYEoG69bR9SDgt449L6heMeySvSlrxs3ptLtT7c4e819ZRw1q226q3Z3u/1lO9Nj7VZ7rf5ZNFNAIERiAwjOtEP4elANqPknkIjEZgWNeJQ3J4NyXtc8U7M35wUn+M3SX5g6T7fs2vESAwHgLDuE5UZ40TknaNOCPjL0na12LcK+O/k1yVtHk8AT4YGgECBAgQmHaBbXOAn0naB4AatqJnd9pvLwKxVAH0q3PW313vUuP3XGS73iJAYDgCw7hO9HMkCqD9KJmHwGgEhnmdeGwO8byk+xmivvev+7r+4LrYZ5e8rREgMGSBYV0nds5xnZJ0rwk1Xg9y7U6r68TbkyqaagQIECBAgMAMCGyYY3xjUk9Y7X4oqPHTk7oNfrG2VAH08iw8d739vlYAXUzeewSGJ7DW14l+jkQBtB8l8xAYncAwrxM75TDrOwWvSOZ+pjg50x6faAQIjJ/AsK4TVdSsnp/nJnOvEbdk2teThyYaAQIEBibgrykDo7QiAkMR2D1bqQciXZv8IDkjqQ8JGgECBJqA60STMCRAYCGBYV0n6neNfZL7J1UMrc8uP0k0AgTGX2BY14ntQ1Hf+blj8sOknvh+daIRIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAjMlsAGs3W4jpYAAQIECBAgQGCGBbbJsb8x2bBn8IEMT+mNzx3slQmv7k28OcM/Ti7pvTYgQIAAAQIECBAgQIAAAQIECBAgQIDAWAr8Rfbq1l7OyHDzefZy40w7tTdPzfumeeYxiQABAgQIECBAgAABAgQIECBAgAABAmMnsEn26FtJK4K+fZ49rIJne/8rGb/TPPOYRIAAAQIECBAgQIAAAQIECBAgQIAAgbEUuE/26tqkipy3JI9KWjsoI3XLe713abJrohEgQIAAAQIECBAgQIAAAQIECBAgQGCiBF6Vva0iZ+X7yabJVsnPkjb92RnXCBAgQIAAAQIECBAgQIAAAQIECBAgMHEC9TDQzySt2PmnGT+y8/qdGdcIECBAgAABAgQIECBAgAABAgQIECAwsQI7Zc8vSqoIemNvWOOnJ5slGgECBAgQIECAAAECBAgQIECAAAECBCZa4FnZ+9YLtIZXJ/tP9BHZeQIECBAgQIAAAQIECBAgQIAAAQIECPQENsrwzKQVQU/LeE3TCBAgQIAAAQIECBAgQIAAAQIECBAgMPECf5IjaMXPNqxpGgECBAgQIECAAAECBAgQIECAAAECBCZa4CHZ+/bdn+dk/NykiqA1rd7TCBAgQIAAAQIECBAgQIAAAQIECBAgMJECm2evf5C0Xp9Py/gzO6/rvZpHI0CAAAECBAgQIECAAAECBAgQIECAwMQJvCd73IqfR3b2/iOd6TWPRoAAAQIECBAgQIAAAQIECBAgQIAAgYkSeHr2thU/69b3bTp7v13GL+i8X/NqBAgQIECAAAECBAgQIECAAAECBAgQmAiBHbKXSxU4n5N5WoG05q1lNAIECBAgQIAAAQIECBAgQIAAAQIECIy9wLHZw1bc7N76PnfHP9aZr5bRCBAgQIAAAQIECBAgQIAAAQIECBAgMNYCr8jeteJnPfF920X2tnp9XtyZ/+WLzOstAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECAwfQL/P5nIGBm2e+uLAAAAAElFTkSuQmCC" title="plot of chunk unnamed-chunk-4" alt="plot of chunk unnamed-chunk-4" width="672" /></p>
<pre class="r"><code>plot(e ~ x)
abline(h = 0)</code></pre>
<p><img 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BAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIEliOw7XIOcgyBFQg8KMe+PNluBWM4lAABAgQIECBAgAABAgQIECDQF4HrMtG3JTf0ZcJtz3NN2wMaj8ASAlX8fO0SfbxNgAABAgQIECBAgAABAgQIECBwl8DF2f3IXb/aG0dAAXQcLX3bEBjc+flXGezzbQxoDAIECBAgQIAAAQIECBAgQIBARwXWZl6PTAb1lI5Oc7LTUgCdrK/RFxeo4udJi7/tHQIECBAgQIAAAQIECBAgQIBA7wWq+FnRViBwjxUc61ACBAgQIECAAAECBAgQIECAAAECBAjMtIAC6Ewvj4sjQIAAAQIECBAgQIAAAQIECBAgQGAlAgqgK9FzLAECBAgQIECAAAECBAgQIECAAAECMy2gADrTy+PiCBAgQIAAAQIECBAgQIAAAQIECBBYiYAC6Er0HEuAAAECBAgQIECAAAECBAgQIECAwEwLKIDO9PK4OAIECBAgQIAAAQIECBAgQIAAAQIEViKgALoSPccSIECAAAECBAgQIECAAAECBAgQIDDTAgqgM708Lo4AAQIECBAgQIAAAQIECBAgQIAAgZUIKICuRM+xBAgQIECAAAECBAgQIECAAAECBAjMtIAC6Ewvj4sjQIAAAQIECBAgQIAAAQIECBAgQGAlAgqgK9FzLAECBAgQIECAAAECBAgQIECAAAECMy2wZqavzsURIECAAAECBAgQaEfgnhnm4OT+yQ3Jd5J/SjQCBAgQIECAAIGOC7gDtOMLbHoECBAgQIAAgZ4LPDDzf09yVXJR8pnknOSHyd8lz0+2TTQCBAgQIECAAIGOCiiAdnRhTYsAAQIECBAgQODO4uY/xuE3kvskddfnZ5Nzk43JzycfTs5K9kg0AgQIECBAgACBDgoogHZwUU2JAAECBAgQIEBgm2NjUMXNnZM/Tx6WPDh5UlKFz72SFydXJk9OPpfcK9EIECBAgAABAgQ6JqAA2rEFNR0CBAgQIECAAIFtHhqDP2ocXpXt85KLm98Hm7oD9NTkkUm9d1hycqIRIECAAAECBAh0TEABtGMLajoECBAgQIAAAQLb/H4Mdkjel5y4hMcP8v6zkpuSFyUPTzQCBAgQIECAAIEOCSiAdmgxTYUAAQIECBAgQGCb3WNQBc1bk+NH9Ph2+p2S1JchVRFUI0CAAAECBAgQ6JCAAmiHFtNUCBAgQIAAAQIEtnl8DNYkX0zqm95HbX/RdPzFUQ/QjwABAgQIECBAYD4EFEDnY51cJQECBAgQIECAwGgC+zbd6tvfx2nfajo/cJyD9CVAgAABAgQIEJh9AQXQ2V8jV0iAAAECBAgQIDC6QD36Xm27zZuRf9Zdo9Vu27zxkwABAgQIECBAoCsCCqBdWUnzIECAAAECBAgQKIHLGoZDxuQ4tOn//8Y8TncCBAgQIECAAIEZF1AAnfEFcnkECBAgQIAAAQJjCfxNet+YPDo5eIwj1zZ9Pz3GMboSIECAAAECBAjMgYAC6BwskkskQIAAAQIECBAYWWBjen4wqW90/x/JKP/erS9OekFyc/KBRCNAgAABAgQIEOiQwCj/IOzQdE2FAAECBAgQIECgBwK/mzn+U/LU5I+SrX0eaN0puj6pfxe/Lbks0QgQIECAAAECBDokoADaocU0FQIECBAgQIAAgTsFrsrPZyd1N+iLk/OS5yX3SgbtZ7NzYvLF5L7J6cnvJBoBAgQIECBAgEDHBAbfdtmxaZkOAQIECBAgQIBAzwW+kPk/IfloUl9w9JFkU3JNskuyU1LtjuSk5LXNfjYaAQIECBAgQIBAlwTcAdql1TQXAgQIECBAgACBhQJ15+fPJL+Z1J2etyV7JVX8/EHyv5KHJ69M6j2NAAECBAgQIECggwLuAO3gopoSAQIECBAgQIDAvwjckr33NKkvRrpPckNSj8drBAgQIECAAAECPRBQAO3BIpsiAQIECBAgQIDAnQL1CHx9OZJGgAABAgQIzKbAYbmsxyf7JPUfK7+TnJXUR9hoBJYtoAC6bDoHEiBAgAABAgQIECBAgAABAgQItCDwjIzxlqS+pHDLdnte+NPk+OTyLd/0O4FRBBRAR1HShwABAgQIECBAgAABAgQIECBAoG2B+m6adySvaAa+Itszk0uT+szun0t+KTk2OTp5dvL5RCNAgMBMC5yYq6vHzwb/x22mL9bFESBAgAABAgQIECBAgAABAhMTqLs+q0ZwU/JbyXbJlu1BeeGMpPpdn9Rj8n1q6zLZmvvaPk267bn6Fvi2RY1HgAABAgQIECBAgAABAgQIECCwlEB91ufrk1uTo5I/bPaz+Yl2WX57VvLBZJekHodXzwqCNrqAP5jRrfQkQIAAAQIECBAgQIAAAQIECBBoR+D3mmH+e7afWWLIugPy15NLkkOS5yUagZEFFEBHptKRAAECBAgQIECAAAECBAgQIECgBYH7ZYwjk3r0/Z0jjndL+r296asAOiKabpsFFED9JRAgQIAAAQIECBAgQIAAAQIECKymQH25UdWkvpTU53qO2j7ddHzUqAfoR6AEFED9HRAgQIAAAQIECBAgQIAAAQIECKymQN0BWu37mzcj/xz0Hxw/8oE69ltAAbTf62/2BAgQIECAAAECBAgQIECAAIHVFriuOeG9xzzxoP/g+DEP172vAgqgfV158yZAgAABAgQIECBAgAABAgQITEfgH5rTHpHtOLWpxzbHDY6fztU769wJjPNHNneTc8EECBAgQIAAAQIECBAgQIAAAQIzJ/DNXNG3k72TfzvG1f1m0/f0MY7RlcBYVXZcBAgQIECAAAECBAgQIECAAAECBNoQeGszyEnZViF0qfar6fCU5EfJ+xKNwMgC7gAdmUpHAgQIECBAgAABAgQIECBAgACBlgROzThfSPZNPpc8NFmsvTRv/FHz5iuzrSKoRmBkgTUj99SRAAECBAgQIECAAAECBAgQIECAQDsCt2eYZydnJ4cnFyR/mpyWXJrslPxcclzyr5Jqb0o+WDsaAQIEZlngxFzcpuQVs3yRro0AAQIECBAgQIAAAQIECBBYFYFdcpb3JrclVS8Ylsvz+nOTPrZ1mXSZrO3j5NuasztA25I0DgECBAgQIECAAAECBAgQIECAwLgCN+SA30jenjwveULygGRj8p3kzGR983s2GoHxBRRAxzdzBAECBAgQIECAAAECBAgQIECAQLsC385wJ7Q7pNEIbBbwJUj+EggQIECAAAECBAgQIECAAAECBAgQ6KyAAmhnl9bECBAgQIAAAQIECBAgQIAAAQIECBBQAPU3QIAAAQIECBAgQIAAAQIECBAgQIBAZwUUQDu7tCZGgAABAgQIECBAgAABAgQIECBAgIACqL8BAgQIECBAgAABAgQIECBAgAABAgQ6K6AA2tmlNTECBAgQIECAAAECBAgQIECAAAECBBRA/Q0QIECAAAECBAgQIECAAAECBAgQINBZAQXQzi6tiREgQIAAAQIECBAgQIAAAQIECBAgoADqb4AAAQIECBAgQIAAAQIECBAgQIAAgc4KKIB2dmlNjAABAgQIECBAgAABAgQIECBAgAABBVB/AwQIECBAgAABAgQIECBAgAABAgQIdFZAAbSzS2tiBAgQIECAAAECBAgQIECAAAECBAgogPobIECAAAECBAgQIECAAAECBAgQIECgswIKoJ1dWhMjQIAAAQIECBAgQIAAAQIECBAgQEAB1N8AAQIECBAgQIAAAQIECBAgQIAAAQKdFVAA7ezSmhgBAgQIECBAgAABAgQIECBAgAABAgqg/gYIECBAgAABAgQIECBAgAABAgQIEOisgAJoZ5fWxAgQIECAAAECBAgQIECAAAECBAgQUAD1N0CAAAECBAgQIECAAAECBAgQIECAQGcFFEA7u7QmRoAAAQIECBAgQIAAAQIECBAgQICAAqi/AQIECBAgQIAAAQIECBAgQIAAAQIEOiugANrZpTUxAgQIECBAgAABAgQIECBAgAABAgQUQP0NECBAgAABAgQIECBAgAABAgQIECDQWQEF0M4urYkRIECAAAECBAgQIECAAAECBAgQIKAA6m+AAAECBAgQIECAAAECBAgQIECAAIHOCqzp7Mxmf2I75BJvXsZl3ifH7NQcd/kyjncIAQIECBAgQIAAAQIECBAgQIAAgd4IuAN0dZf6OTndJ5Orko3JxcmfJI9LRm0fSMfvNRn1GP0IECBAgAABAgQIECBAgAABAgQI9FJAAXR1ln2XnOaDyZ8nT0vul2ybPDR5UfKF5J3J4M7O7GoECBAgQIAAAQIECBAgQIAAAQIECKxUQAF0pYKjHX9Cuh27oOsN2b802dS8VuvwyuTryYHNazYECBAgQIAAAQIECBAgQIAAAQIECKxQQAF0hYAjHH54+rys6VePvv/rZLfkp5I9ktcl1yXVDk4+lyiCBkEjQIAAAQIECBAgQIAAAQIECBAgsFIBBdCVCi59/EvT5Z7JbclTk9OTO5JqVfh8W/IzyflJtQclf53sXb9oBAgQIECAAAECBAgQIECAAAECBAgsX0ABdPl2ox5Zxc1qf5YMipx3vrDgxxXZf2Ly+ea1ugP0E0l9dqhGgAABAgQIECBAgAABAgQIECBAgMAyBRRAlwk3xmE/3fQ9b4ljNuT9pyd/2/R7ZLYfTeruUY0AAQIECBAgQIAAAQIECBAgQIAAgWUIKIAuA23MQ7Zv+t84wnEb0+dZybebvkdl+65m34YAAQIECBAgQIAAAQIECBAgQIAAgTEFFEDHBFtG9281xzxsxGP/Kf2ellzd9K/PEH1Vs29DgAABAgQIECBAgAABAgQIECBAgMAYAgqgY2Ats+ugAPrCHL/niGNckn51J2jdEVrt7cmxd+75QYAAAQIECBAgQIAAAQIECBAgQIDAyAIKoCNTLbtjfflRtfsltT/qt7v/XfpW0bS+MX7b5P3J7yTWLAgaAQIECBAgQIAAAQIECBAgQIAAAQKzI3B2LmVTk2uzrWLmy5NR2kvSqYqgg+NvX7A/yvGz1ufE5vpfMWsX5noIECBAgAABAgQIECBAgAABAjMmsC7XUzWhtTN2XXN1Oe4mXJ3lqiLmhc2p9sj2V5PfaH5fanNKOvyH5LamozVbSsz7BAgQIECAAAECBAgQIECAAAECBBoBxbTV+VP4Tk7z6OTk5IbmlD9otqNsPpBOj0i+OEpnfQgQIECAAAECBAgQIECAAAECBAgQ2CygALp6fwk35VT12PvuyWOS+mKjcdo30vmJya8k9fmgGxKNAAECBAgQIECAAAECBAgQIECAAIGtCKzZynvemoxAPcpeBczltj/JgRWNAAECBAgQIECAAAECBAgQIECAAIElBNwBugSQtwkQIECAAAECBAgQIECAAAECBAgQmF8BBdD5XTtXToAAAQIECBAgQIAAAQIECBAgQIDAEgIegV8CaMbe3i7Xs/eCa7p8wb5dAgQIECBAgAABAgQIECBAgAABAgS2EFAA3QJkxn89LNf31QXXuO2C/UnuviSDvyxp447hfZsLPWSSF2xsAgQIECBAgAABAgQIECBAgAABAiWgAOrvYBSBx6XToaN0HKPPz47RV1cCBAgQIECAAAECBAgQIECAAAECyxJQAF0WW+8OenFm/JakjTtOP5pxHpZckWgECBAgQIAAAQIECBAgQIAAAQIEJiqgADpR3tYHPz8j3r/1UZce8NZ0uWjpbiP1uGmkXjoRIECAAAECBAgQIECAAAECBAgQaEFAAbQFxFUc4rac66pVPJ9TESBAgAABAgQIECBAgAABAgQIEJhrgTa+1GauAVw8AQIECBAgQIAAAQIECBAgQIAAAQLdFVAA7e7amhkBAgQIECBAgAABAgQIECBAgACB3gt4BH76fwL75BL2THZuUp+ReV2yIbkm8ZmZQdAIECBAgAABAgQIECBAgAABAgQILEdAAXQ5ais7ZtccfmzywuSQpH5frNVnfl6YnJN8PDkz2ZRoBAgQIECAAAECBAgQIECAAAECBAgQmCmBvXM1Jyd1Z2cVMZeTKoYencxzOy8XX3NfP8+TcO0ECBAgQIAAAQIECBAgQIAAgVUQWJdzVB1l7Sqcq7OncAfo6iztHjnN2cmhC05Xf7xXJJclVycbk5uTWpMdk92S/ZL9kx2SanXH6OnJq5OTEo0AAQIECBAgQIAAAQIECBAgQIAAAQJTFdglZ/9yUgXPyrnJMcl9k1Hadun0uOSU5JZkMM5R2Z/H5g7QeVw110yAAAECBAgQIECAAAECBAhMQ8AdoNNQd86xBY7LEYOi5Yeyf4+xR7jrgCp6DoqgF6xwrLtGXd09BdDV9XY2AgQIECBAgAABAgQIECBAYH4FFEBbWLuVFONaOH0vhnhsM8sqWNaXH92xglnXlyC9pjm+Hqc/cAVjOZQAAQIECBAgQIAAAQIECBAgQIBA5wUUQCe/xPX4erUzklvv3FvZj48tOPzgBft2CRAgQIAAAQIECBAgQIAAAQIECBDYQkABdAuQCfy6bzPm91oa+5qMMyik7tTSmIYhQIAAAQIECBAgQIAAAQIECBAg0EkBBdDJL+slzSke09Kp6pH6+mKkal/bvPGTAAECBAgQIECAAAECBAgQIECAAIFhAgqgw1Tafa2+9Kfa85Mj79xb/o/dc+g7msOvzfbS5Q/lSAIECBAgQIAAAQIECBAgQIAAAQLdF1AAnfwavzmnqEfWd0xOS16SbJ+M2w7PAWclta323s0bPwkQIECAAAECBAgQIECAAAECBAgQWExgzWJveL01gXoE/g3J25J7J1W4rP3PJ19P6i7Oq5KNyU1JrUkVS3dL9ksekjwxOSQZtCqEvnHwiy0BAgQIECBAgAABAgQIECBAgAABAgSmLXBcLuDGZNMK88kcv2cyr60+EqAM1s/rBFw3AQIECBAgQIAAAQIECBAgQGCVBNblPFVHWbtK5+vkaTwCv3rL+v6cav/khOTKMU97c/rX4/PPTJ6e1Od/agQIECBAgAABAgQIECBAgAABAgQILCHgEfglgFp+++qMd3yTA7I9Ijkoqcfd6/H4XZP6vNDrkw1JPT5/UXJ+Uq9pBAgQIECAAAECBAgQIECAAAECBAiMIaAAOgZWy12/m/EqGgECBAgQIECAAAECBAgQIECAAAECExLwCPyEYA1LgAABAgQIECBAgAABAgQIECBAgMD0BRRAp78GroAAAQIECBAgQIAAAQIECBAgQIAAgQkJKIBOCNawBAgQIECAAAECBAgQIECAAAECBAhMX0ABdPpr4ApmT2CHXNLeyT1n79JcEQECBAgQIECAAAECBAgQIECAwDgCCqDjaOnbZYEHZXLvTC5JbkquTG5JvpYcn+yWaAQIECBAgAABAgQIECBAgAABAgQIENiqwHl5d1Oyfqu9VvfNV+d0VfSs66rU/lXJbc3v9drVyTMSjQABAgQIECBAgAABAgQIECCwWgLrcqKqS6xdrRN28TzuAO3iqprTOAInpvPbk+2T+j8qP5/slNQj8LV9WvLZZK/ktOTYRCNAgAABAgQIECBAgAABAgQIECBAgMBQgVm6A/RFucL6rygbk2cNvdq7Xvwv2a2+NyePuOtlewQIECBAgAABAgQIECBAgACBiQm4A3RitAYmMDmBWSmA7pwp/iCpouavJqO0d6VT9f/rUTrrQ4AAAQIECBAgQIAAAQIECBBYoYAC6AoB63CPwLeAaIi5FKg7Ph+QfCX5QDJKqy9D+nHypOQhoxygDwECBAgQIECAAAECBAgQIECAwHQFFECn6+/s0xN4anPq/z3GJWxI3zOa/oPjxzhcVwIECBAgQIAAAQIECBAgQIAAgdUWUABdbXHnmxWBBzUX8o0xL+jCpv/+Yx6nOwECBAgQIECAAAECBAgQIECAwBQEFECngO6UMyGwprmK28a8mkH/wfFjHq47AQIECBAgQIAAAQIECBAgQIDAagoogK6mtnPNksD3m4s5aMyLOrjpPzh+zMN1J0CAAAECBAgQIECAAAECBAgQWE0BBdDV1HauWRL4bHMxzxnjorZP32c2/QfHj3G4rgQIECBAgAABAgQIECBAgAABAqstoAC62uLONysC63Mh/5w8LXnSiBf1W+n3wKQ+B/TvRzxGNwIECBAgQIAAAQIECBAgQIAAgSkKKIBOEd+ppypwTc7+5uYKPpztYUtczb/J+yc0fV67RF9vEyBAgAABAgQIECBAgAABAgQIECDQU4HzMu9NSd2BOe1W/wHgjKSu5/rk9cnuycK2X355d3JHUv1+L9EIECBAgAABAgQIECBAgAABAqshsC4nqXrE2tU4mXMQINCOwCwVQGtG9bmepyb1f0wqtyRfSz6TXJwMXq9vf3fnZxA0AgQIECBAgAABAgQIECBAYNUEFEBXjdqJCLQnMGsF0MHMfjE7n06qADooeta2Pif0z5KfSTQCBAgQIECAAAECBAgQIECAwGoKKIC2oL2mhTEMQaALAp/NJCq7JQ9O6lH4q5NvJTcnGgECBAgQIECAAAECBAgQIECAwBwKKIDO4aK55IkKbMjo9Qi8RoAAAQIECBAgQIAAAQIECBAg0AEB3wLfgUU0BQIECBAgQIAAAQIECBAgQIAAAQIEhgsogA538SoBAgQIECBAgAABAgQIECBAgAABAh0QUADtwCKaAgECBAgQIECAAAECBAgQIECAAAECwwUUQIe7eJUAAQIECBAgQIAAAQIECBAgQIAAgQ4IKIB2YBFNgQABAgQIECBAgAABAgQIECBAgACB4QIKoMNdvEqAAAECBAgQIECAAAECBAgQIECAQAcEFEA7sIimQIAAAQIECBAgQIAAAQIECBAgQIDAcAEF0OEuXiVAgAABAgQIECBAgAABAgQIECBAoAMCCqAdWERTIECAAAECBAgQIECAAAECBAgQIEBguIAC6HAXrxIgQIAAAQIECBAgQIAAAQIECBAg0AEBBdAOLKIpECBAgAABAgQIECBAgAABAgQIECAwXEABdLiLVwkQIECAAAECBAgQIECAAAECBAgQ6ICAAmgHFtEUCBAgQIAAAQIECBAgQIAAAQIECBAYLqAAOtzFqwQIECBAgAABAgQIECBAgAABAgQIdEBAAbQDi2gKBAgQIECAAAECBAgQIECAAAECBAgMF1AAHe7iVQIECBAgQIAAAQIECBAgQIAAAQIEOiCgANqBRTQFAgQIECBAgAABAgQIECBAgAABAgSGCyiADnfxKgECBAgQIECAAAECBAgQIECAAAECHRBQAO3AIpoCAQIECBAgQIAAAQIECBAgQIAAAQLDBRRAh7t4lQABAgQIECBAgAABAgQIECBAgACBDggogHZgEU2BAAECBAgQIECAAAECBAgQIECAAIHhAgqgw128SoAAAQIECBAgQIAAAQIECBAgQIBABwQUQDuwiKZAgAABAgQIECBAgAABAgQIECBAgMBwAQXQ4S5eJUCAAAECBAgQIECAAAECBAgQIECgAwIKoB1YRFMgQIAAAQIECBAgQIAAAQIECBAgQGC4gALocBevEiBAgAABAgQIECBAgAABAgQIECDQAQEF0A4soikQIECAAAECBAgQIECAAAECBAgQIDBcQAF0uItXCRAgQIAAAQIECBAgQIAAAQIECBDogIACaAcW0RQIECBAgAABAgQIECBAgAABAgQIEBguoAA63MWrBAgQIECAAAECBAgQIECAAAECBAh0QEABtAOLaAoECBAgQIAAAQIECBAgQIAAAQIECAwXUAAd7uJVAgQIECBAgAABAgQIECBAgAABAgQ6IKAA2oFFNAUCBAgQIECAAAECBAgQIECAAAECBIYLKIAOd/EqAQIECBAgQIAAAQIECBAgQIAAAQIdEFAA7cAimgIBAgQIECBAgAABAgQIECBAgAABAsMFFECHu3iVAAECBAgQIECAAAECBAgQIECAAIEOCCiAdmARTYEAAQIECBAgQIAAAQIECBAgQIAAgeECCqDDXbxKgAABAgQIECBAgAABAgQIECBAgEAHBBRAO7CIpkCAAAECBAgQIECAAAECBAgQIECAwHABBdDhLl4lQIAAAQIECBAgQIAAAQIECBAgQKADAgqgHVhEUyBAgAABAgQIECBAgAABAgQIECBAYLiAAuhwF68SIECAAAECBAgQIECAAAECBAgQINABgTUdmMOsT+HqXOC2E7rIvSY0rmEJECBAgAABAgQIECBAgAABAgQIdEJAAXTyy7hnTuFO28k7OwMBAgQIECBAgAABAgQIECBAgACBuwkogN6NpPUXnpAR358cvGDkK7N/+4Lf7RIgQIAAAQIECBAgQIAAAQIECBAgMAEBBdAJoG4x5Jfz+xHJp5JHN++dmu3xzb4NAQIECBAgQIAAAQIECBAgQIAAAQITEvBo9oRgtxj2R/n9l5OLm9d/O9snNfs2BAgQIECAAAECBAgQIECAAAECBAhMSEABdEKwQ4bdkNdenNyRlPu6ZLdEI0CAAAECBAgQIECAAAECBAgQIEBgQgIKoBOCXWTYv83r72re2yfbly/Sz8sECBAgQIAAAQIECBAgQIAAAQIECLQgoADaAuKYQ9Rnf17aHPOqbO815vG6EyBAgAABAgQIECBAgAABAgQIECAwooAvQRoRqsVuN2SsFyTPbMY8MNsLm30bAgQIECBAgAABAgQIECBAgAABAgRaFFAAbRFzjKHOSd+KRoAAAQIECBAgQIAAAQIECBAgQIDABAU8Aj9BXEMTIECAAAECBAgQIECAAAECBAgQIDBdAQXQ6fo7OwECBAgQIECAAAECBAgQIECAAAECExRQAJ0grqEJECBAgAABAgQIECBAgAABAgQIEJiugALodP2dnQABAgQIECBAgAABAgQIECBAgACBCQr4EqQJ4k5g6O0y5t4Lxr18wf4kd++dwR+dbNvCSXZtYQxDECBAgAABAgQIECBAgAABAgQIEBhJQAF0JKaZ6XRYruSrC66mjYLkguEW3f3jvPPsRd9d3hv7Lu8wRxEgQIAAAQIECBAgQIAAAQIECBAYXUABdHSrPvf8cCa/S9LGRyYckXF2S65NNAIECBAgQIAAAQIECBAgQIAAAQITFVAAnShvZwb/i8yk0kY7L4P8XHJjG4MZgwABAgQIECBAgAABAgQIECBAgMDWBBRAt6Yze++dn0u6/+xdlisiQIAAAQIECBAgQIAAAQIECBAgMJsCCqCzuS6LXdVteeOqxd70OgECBAgQIECAAAECBAgQIECAAAECPynQxmc6/uSIfiNAgAABAgQIECBAgAABAgQIECBAgMCMCLgDdPoLsU8uYc9k5yY3ZXtdsiG5JqnfNQIECBAgQIAAAQIECBAgQIAAAQIEliGgALoMtBUesmuOPzZ5YXJIUr8v1uqR9wuTc5KPJ2cmmxKNAAECBAgQIECAAAECBAgQIECAAAECMyWwd67m5KTu7Kwi5nJSxdCjk3lu9S3wNff18zwJ106AAAECBAgQIECAAAECBAgQWAWBdTlH1VHWrsK5OnsKd4CuztLukdOcnRy64HT1x3tFcllydbIxuTmpNdkx2S3ZL9k/2SGpVneMnp68Ojkp0QgQIECAAAECBAgQIECAAAECBAgQIDBVgV1y9i8nVfCsnJsck9w3GaVtl06PS05JbkkG4xyV/Xls7gCdx1VzzQQIECBAgAABAgQIECBAgMA0BNwBOg115xxb4LgcMShafij79xh7hLsOqKLnoAh6wQrHumvU1d1TAF1db2cjQIAAAQIECBAgQIAAAQIE5ldAAbSFtVtJMa6F0/diiMc2s6yCZX350R0rmHV9CdJrmuPrcfoDVzCWQwkQIECAAAECBAgQIECAAAECBAh0XkABdPJLXI+vVzsjufXOvZX9+NiCww9esG+XAAECBAgQIECAAAECBAgQIECAAIEtBBRAtwCZwK/7NmN+r6Wxr8k4g0LqTi2NaRgCBAgQIECAAAECBAgQIECAAAECnRRQAJ38sl7SnOIxLZ2qHqmvL0aq9rXNGz8JECBAgAABAgQIECBAgAABAgQIEBgmoAA6TKXd1+pLf6o9Pznyzr3l/9g9h76jOfzabC9d/lCOJECAAAECBAgQIECAAAECBAgQINB9AQXQya/xm3OKemR9x+S05CXJ9sm47fAccFZS22rv3bzxkwABAgQIECBAgAABAgQIECBAgACBxQTWLPaG11sTqEfg35C8Lbl3UoXL2v988vWk7uK8KtmY3JTUmlSxdLdkv+QhyROTQ5JBq0LoGwe/2BIgQIAAAQIECBAgQIAAAQIECBAgQGDaAsflAm5MNq0wn8zxeybz2uojAcpg/bxOwHUTIECAAAECBAgQIECAAAECBFZJYF3OU3WUtat0vk6exiPwq7es78+p9k9OSK4c87Q3p389Pv/M5OlJff6nRoAAAQIECBAgQIAAAQIECBAgQIDAEgIegV8CqOW3r854xzc5INsjkoOSety9Ho/fNanPC70+2ZDU4/MXJecn9ZpGgAABAgQIECBAgAABAgQIECBAgMAYAgqgY2C13PW7Ga+iESBAgAABAgQIECBAgAABAgQIECAwIQGPwE8I1rAECBAgQIAAAQIECBAgQIAAAQIECExfQAF0+mvgCggQIECAAAECBAgQIECAAAECBAgQmJCAAuiEYA1LgAABAgQIECBAgAABAgQIECBAgMD0BRRAp78GroAAAQIECBAgQIAAAQIECBAgQIAAgQkJKIBOCNawBAgQIECAAAECBAgQIECAAAECBAhMX0ABdPpr4AoIECBAgAABAgQIECBAgAABAgQIEJiQgALohGANS4AAAQIECBAgQIAAAQIECBAgQIDA9AUUQKe/Bq6AAAECBAgQIECAAAECBAgQIECAAIEJCSiATgjWsAQIECBAgAABAgQIECBAgAABAgQITF9AAXT6a+AKCBAgQIAAAQIECBAgQIAAAQIECBCYkIAC6IRgDUuAAAECBAgQIECAAAECBAgQIECAwPQFFECnvwaugAABAgQIECBAgAABAgQIECBAgACBCQkogE4I1rAECBAgQIAAAQIECBAgQIAAAQIECExfQAF0+mvgCggQIECAAAECBAgQIECAAAECBAgQmJCAAuiEYA1LgAABAgQIECBAgAABAgQIECBAgMD0BRRAp78GroAAAQIECBAgQIAAAQIECBAgQIAAgQkJKIBOCNawBAgQIECAAAECBAgQIECAAAECBAhMX0ABdPpr4AoIECBAgAABAgQIECBAgAABAgQIEJiQgALohGANS4AAAQIECBAgQIAAAQIECBAgQIDA9AUUQKe/Bq6AAAECBAgQIECAAAECBAgQIECAAIEJCSiATgjWsAQIECBAgAABAgQIECBAgAABAgQITF9AAXT6a+AKCBAgQIAAAQIECBAgQIAAAQIECBCYkIAC6IRgDUuAAAECBAgQIECAAAECBAgQIECAwPQFFECnvwaugAABAgQIECBAgAABAgQIECBAgACBCQkogE4I1rAECBAgQIAAAQIECBAgQIAAAQIECExfQAF0+mvgCggQIECAAAECBAgQIECAAAECBAgQmJCAAuiEYA1LgAABAgQIECBAgAABAgQIECBAgMD0BRRAp78GroAAAQIECBAgQIAAAQIECBAgQIAAgQkJKIBOCNawBAgQIECAAAECBAgQIECAAAECBAhMX0ABdPpr4AoIECBAgAABAgQIECBAgAABAgQIEJiQwJoJjWtYAgQIECBAgAABAgT6K/CgTP25yROTfZKbk0uTTyZ/ldyYaAQIECBAgAABAgQ6KXBeZrUpWd/J2ZkUAQIECBAgQKDfAjtk+u9MquBZ/+Yblu/n9WMSjQABAgQIEFhaYF261P8/Xbt0Vz0WE3AH6GIyXidAgAABAgQIECBAYByBe6fzp5IjktuTDyd/mXwnqcLo4cmvJI9KPpQcmhyfaAQIECBAgAABAgQ6JeAO0E4tp8kQIECAAAECBO4U2DY/z0zqDpUqeFaxc7H2a3ljcIfory/WyesECBAgQIDAnQLuAPWHQGAOBRRA53DRXDIBAgQIECBAYAmBF+T9Kn5eldTnfy7VBv03pON9l+rsfQIECBAg0GMBBdAWFt+3wLeAaAgCBAgQIECAAAECPRd4XTP/2l42gkU9An96smvy0hH660KAAAECBAgQWLaAAuiy6RxIgAABAgQIECBAgEAE6o7PeuT9uuTPklHbyU3HZ416gH4ECBAgQIAAgeUIKIAuR80xBAgQIECAAAECBAgMBH662Tk321sHL46w/XLT56Ej9NWFAAECBAgQILBsAQXQZdM5kAABAgQIECBAgACBCNS3v1erO0DHaden823JLsmacQ7UlwABAgQIECAwjoAC6Dha+hIgQIAAAQIECBAgsKXAD5sX9tnyjSV+v1/er8LntUkVQjUCBAgQIECAwEQEFEAnwmpQAgQIECBAgAABAr0RuCAzrUffH5XsMcasn9r0/eoYx+hKgAABAgQIEBhbQAF0bDIHECBAgAABAgQIECCwQODH2T872S557YLXt7Z7z7w5+Ob4P99aR+8RIECAAAECBAgQmDeB83LBm5L183bhrpcAAQIECBAgQGBRgbr7846k7gQd3Nm5aOe88a6k/k347aQKpxoBAgQIECAwXGBdXq7/n7l2+NteHUXAHaCjKOlDgAABAgQIECBAgMDWBL6SN/9bUp/peXryymRYYfP+ef0jycuTm5MXJlU01QgQIECAAAECExPwbYsTozUwAQIECBAgQIAAgV4JvCmz3Smpx+Dfmbwm+UTynWSH5BHJU5LqsyE5Jjkn0QgQIECAAAECBAh0SsAj8J1aTpMhQIAAAQIECNxN4Ki8cmFSj+ttmXpMvj7z88GJRoAAAQIECCwt4BH4pY2W7OEO0CWJdCBAgAABAgQIECBAYAyBM9O38vDkick+ST3ufmny6eTKRCNAgAABAgQIrJqAAuiqUTsRAQIECBAgQIAAgV4JnJ/ZVjQCBAgQIECAwFQFfAnSVPmdnAABAgQIECBAgAABAgQIECBAgACBSQoogE5S19gECBAgQIAAAQIECBAgQIAAAQIECExVQAF0qvxOToAAAQIECBAgQIAAAQIECBAgQIDAJAUUQCepa2wCBAgQIECAAAECBAgQIECAAAECBKYqoAA6VX4nJ0CAAAECBAgQIECAAAECBAgQIEBgkgIKoJPUNTYBAgQIECBAgAABAgQIECBAgAABAlMVUACdKr+TEyBAgAABAgQIECBAgAABAgQIECAwSQEF0EnqGpsAAQIECBAgQIAAAQIECBAgQIAAgakKKIBOld/JCRAgQIAAAQIECBAgQIAAAQIECBCYpIAC6CR1jU2AAAECBAgQIECAAAECBAgQIECAwFQF1kz17E5OgAABAgQIECBAgACBzQJ7ZbM2eXpyQLJD8v3kC8mfJt9INAIECBAgQIDA2AIKoGOTtX7APhlxz2TnJjdle12yIbkmqd81AgQIECBAgAABAl0WeEUm97vJbltMcv/8/tjkdcm65OXJ9YlGgAABAgQIECAwwwK75tpelnw5qSLnpq3k1rz398l7kqOTbZN5b+dlAjXn9fM+EddPgAABAgQIECCwYoH69+2pyeDfxB/P/nOTg5Mqfv5S8u5kY1J9Lkj2SjQCBAgQINAXgfoPgPX/A+spCY3AzAvsnSs8OVmq6Dn4x9+w7YU5vgqh89wUQOd59Vw7AQIECBAgQKBdgeMzXP27t/6N/MytDP3gvPeNpPp+LvFdBkHQCBAgQKAXAgqgLSyzR+BbQBxhiD3S5+zk0AV96x9vVySXJVcn9V+1b05qTXZM6vGf/ZL9k/r8o2qHJKcnr05OSjQCBAgQIECAAAEC8ypQ/859Y3JH8pzkrGSxdkneeHLy1eTI5EXJBxONAAECBAgQIEBgBgR2yTXU4+5V8KycmxyT3DcZpW2XTo9LTkluSQbjHJX9eWzuAJ3HVXPNBAgQIECAAIH2Bd6aIevftuMUMl/QHFOPwmsECBAgQKAPAu4A7cMqd2COx2UOg6Llh7K/ksd1qug5KILWP/pWMlYOn0pTAJ0Ku5MSIECAAAECBGZO4KJcUf07uf5j/6itnpb6UVLHPWjUg/QjQIAAAQJzLKAA2sLizWMBrYVpr+oQ9a2V1apgeWxSj/gst52ZA1/THFyP0x+43IEcR4AAAQIECBAgQGCKAtvm3PW5nlXI/MoY13Fb+taXhFZ7yOaNnwQIECBAgACBrQsogG7dp413B/9F+4wMdmsLA35swRj17ZgaAQIECBAgQIAAgXkT2D4XXKmnmyrjtH9uOu86zkH6EiBAgAABAv0VUACd/Nrv25ziey2d6pqMMyik7tTSmIYhQIAAAQIECBAgsJoC9eWfP07qyz5H/Wz8wfUNHn2/cvCCLQECBAgQIEBgawIKoFvTaee9+sbKao/ZvFnxz3qkvr4YqdrXNm/8JECAAAECBAgQIDB3Auc0V3z0GFe+T/oentyY+CKkMeB0JUCAAAECfRZQAJ386p/XnOL52R65wtPtnuPf0YxxbbaXrnA8hxMgQIAAAQIECBCYlsCHmxP/drb1OPwo7Y3pVJ8fWh8vtXGUA/QhQIAAAQIECBCYvEB9uHt9rlF9wHs95vOSZNR/4KXrv7T6L93nJjVO5feTeWxVEK7rXz+PF++aCRAgQIAAAQIEWhOob3S/OKl/G34gWermjLVN3/o4qIcmGgECBAgQ6IOAb4FvYZXrHx3aZAXqEfg3JG9L7p28t9n/fLZfTy5Nrkrqv2DflNSa7JjsluyX1LdbPjE5JBm0s7JT//VbI0CAAAECBAgQIDCvAvWN7lo+NPQAAEAASURBVMckX0p+Jbl/8vLk28nCVv8uPj55bfPiK7L9ZrNvQ4AAAQIECBAgMEMCx+Va6rOK6r9wrySfzPF7JvPa3AE6ryvnugkQIECAAAECkxF4fIb9YVL/Rr49+WLy7qQ++umvkuuTeq8Kpq9MNAIECBAg0CcBd4D2abU7Mtf6hst6dP2KZJwiaN0ZWv/4e0Yy700BdN5X0PUTIECAAAECBNoXqLs/T0nqqagt/518R177P8mjEo0AAQIECPRNQAG0hRX3CHwLiGMMcXX61uM7lQOSI5KDknqspx6P3zWpzzSq/8q9IanH5y9Kzk/qNY0AAQIECBAgQIBAFwWuzKTqs/JflfxCckCyQ/KD5AvNNhuNAAECBAgQIDC+wKQLoHXHYxX4KlXcq0dZqj04+X5Sdzb2tX03E69oBAgQIECAAAECBAhsFrghm0/AIECAAAECBAi0KbDUNy0u91zH5MDvJvVZPl9KPpC8KRm012TnsuRNyXaJRoAAAQIECBAgQIAAAQIECBAgQIAAgdYF2i6AHpgrrA8t/1Cy/1au9oC8V3eH/k7yl8lOiUaAAAECBAgQIECAAAECBAgQIECAAIFWBdosgNbj9B9J6lscq/1z8qmkPrB8y/a9BS8cnf3/ueB3u4sL1N2y+y7I4j29Q4AAAQIECBAgQIAAAQIECBAgQIDANm1+BmjdzfmoxvTUbF+bXJu8OHlysrD9en55X1LfbP6A5EXJCcm3Em1xgcPy1lcXvL3tgv1J7j4ng9c6tlEwf0hzoU/I9tPNvg0BAgQIECBAgAABAgQIECBAgMDdBQ65+0teGVegrQJojVOf61mtilq/ltxRv2ylnZv3qjB6QXLP5D8mr0+02ROoz3R9WsuXtVfGe0rLYxqOAAECBAgQIECAAAECBAgQIECAwE8ItFUAfWhG3bEZ+dXZLlX8HFzERdk5Lfl3ycGDF21nTqDu/jwlaeOO03dnnIOSLyW/l2gECBAgQIAAAQIECBAgQIAAAQLDBV6Xl39p+FteHVWgrQLo4c0J63M/Lx715E2/ugO0CqA/NeZxfex+fiZ9/ylM/Lqc8+yWzlt/I9V+mJx1554fBAgQIECAAAECBAgQIECAAAECwwTqYyO1FQq0VQDdobmOW7Id9e7PwaXv2uzcMHjBdlGB2/LOVYu+6w0CBAgQIECAAAECBAgQIECAAAECBH5CoI0vtakB687EavdJ9rtzb/Qfj2y6fmP0Q/QkQIAAAQIECBAgQIAAAQIECBAgQIDA0gJtFUCreHl7c7r6NvhRW32xzi80nRVAR1XTjwABAgQIECBAgAABAgQIECBAgACBkQTaegT+ppxtffLcpL4w5x+SdyRbexz+F/P++5NqNyYfv3Ovfz/2yZT3THZuUpb1mZsbkmuS+l0jQIAAAQIECBAgQIAAAQIECBAgQGAZAm0VQOvUL00enzwgeWtSxdDTksGX9tQ3iNeXJT0ieXpS7w/aG7LzncEvHd/WZ54em7wwOSQZfAZqdu/W6jM/L0zOSapAfGayKdEIECBAgAABAgQIECBAgAABAgQIEJiCwC/nnPUt31WkGzWfSN8qjna97Z0JnpzUnZ2j2mzZr4qhRyfz3M7Lxde86o5hjQABAgQIECBAgAABAgQIECBAYHGBdXmr6ihrF+/inaUE2rwDtM51dvLTyVuSWpitFTavzPuvTwYLmd3Otj0ys7I5dMEM64/3iuSy5OpkY3JzUmuyY7JbUl8otX+yQ1Kt7hg9PXl1clKiESBAgAABAgQIECBAgAABAgQIECCwFYG2C6B1qh8k9Yj3O5PHJgc1uW+2lyb/2KQKeXU3ZNfbLplg3eU6KH5+Jftl89dJFT6Xatulw6OTMj0uqd9PTMqxHonXCBAgQIAAAQIECBAgQIAAAQIECBAgMDWBKlrW3Z6VDyX3SJbbjsqBtyQ11gXJSsbK4VNpHoGfCruTEiBAgAABAgQIECBAgAABAnMoMHhy2iPwK1i8eSygrWC6Uzm07oKtVgXLuovzjvplma3u+HxNc2zdUXrgMsdxGAECBAgQIECAAAECBAgQIECg7wL1ZPSeydY+wrHvRp2YvwLo5Jfxcc0pzsj21hZO97EFYxy8YN8uAQIECBAgQIAAAQIECBAgQIDA1gUemLf/IPlmUt/Fck2zPTfb1yX3SrSOCSiATn5B921O8b2WTlX/wxwUUndqaUzDECBAgAABAgQIECBAgAABAgS6LvCfM8FvJVXorC/xrqd0r03qTtBHJVUYvSR5WqJ1SEABdPKLWf/DqfaYzZsV/6xH6uuLkKp9bfPGTwIECBAgQIAAAQIECBAgQIAAga0IvDXv/WGyY/Lh5PHN/n2y3Tl5ZvI3yf2Sjyf/PtEIEBhR4H3pV19atDE5csRjFuu2e96oomeNV3eCzmM7Lxdd179+Hi/eNRMgQIAAAQIECBAgQIAAAQJzJ1DFzKpF3JQ8e4mr/69N36rjHLZE39V425cgrYayc6xY4MEZ4Zak/of24+QlyfbJuO3wHFCfR1HjVH4/mcemADqPq+aaCRAgQIAAAQIECBAgQIDAfArUxwdenlQt5cUjTuE9Tf+zR+w/yW4KoC3o1mccaJMVqEfg35C8Lbl38t5m//PZfj25NLkqqf+yUP8lotakbsfeLdkveUjyxOSQZNDOys4bB7/YEiBAgAABAgQIECBAgAABAgQIDBWoR9vri4/qhqw/Htrj7i/+l7z0guTJSd3YVrUdjQCBEQSOS58bk8EdnMvdfjJj7DnC+Wa1iztAZ3VlXBcBAgQIECBAgAABAgQIEOiewKmZUtVgXjHm1AZ3Xv7mmMe13X1wHWvbHrhP4/kSpNVb7ffnVPsnJyRXjnnam9P/tKT+q8XTk/qGMo0AAQIECBAgQIAAAQIECBAgQGDrAlWLqXbB5s3IPwf9Dxj5CB1nVsAj8Ku7NFfndMc3OSDbI5KDknrcvR6P3zW5Nbk+2ZDULdYXJecn9ZpGgAABAgQIECBAgAABAgQIECAwusB2Tdeqt4zTbms6D44f51h9Z0xAAXR6C/LdnLqiESBAgAABAgQIECBAgAABAgQITEbg+82wdQPaF8c4RX0nS7XLN2/8nGcBj8DP8+q5dgIECBAgQIAAAQIECBAgQIAAga0JfK5589lb67TFe3XX57Oa1z63xXt+nUMBBdA5XDSXTIAAAQIECBAgQIAAAQIECBAgMJLA+vSqjxU8KjlypCO22eY/pd++yf9N6suctTkXUACd8wV0+QQIECBAgAABAgQIECBAgAABAosK1Pex/EHz7keyfdiiPTe/8Yxs3tL0ed0Sfb1NgACBoQL1X042JfVfYDQCBAgQIECAAAECBAgQIECAwKQF7pkTfDKpekR96fSrkvoi6oXtAfnlxOT2pPqdkMxCW5eLqOtZOwsX4xoIEBhNQAF0NCe9CBAgQIAAAQIECBAgQIAAgfYEdsxQg2JiFRRvSs5NPp1ckNyR1OtVAH1DMittcM0KoLOyIq6DwAgCCqAjIOlCgAABAgQIECBAgAABAgQITETgKRn1M8ltSRU8B7kh+x9NDk1mqSmAtrAaa1oYwxAECBAgQIAAAQIECBAgQIAAAQIE5kHgrFxkZY/koGT3pD4n9JvJxkTroIACaAcX1ZQIECBAgAABAgQIECBAgAABAgS2KvCjvFuPwGs9EPAt8D1YZFMkQIAAAQIECBAgQIAAAQIECBAg0FcBBdC+rrx5EyBAgAABAgQIECBAgAABAgQIEOiBgAJoDxbZFAkQIECAAAECBAgQIECAAAECBAj0VUABtK8rb94ECBAgQIAAAQIECBAgQIAAAQIEeiCgANqDRTZFAgQIECBAgAABAgQIECBAgAABAn0VUADt68qbNwECBAgQIECAAAECBAgQIECAAIEeCCiA9mCRTZEAAQIECBAgQIAAAQIECBAgQIBAXwUUQPu68uZNgAABAgQIECBAgAABAgQIECBAoAcCCqA9WGRTJECAAAECBAgQIECAAAECBAgQINBXAQXQvq68eRMgQIAAAQIECBAgQIAAAQIECBDogYACaA8W2RQJECBAgAABAgQIECBAgAABAgQI9FVAAbSvK2/eBAgQIECAAAECBAgQIECAAAECBHogoADag0U2RQIECBAgQIAAAQIECBAgQIAAAQJ9FVAA7evKmzcBAgQIECBAgAABAgQIECBAgACBHggogPZgkU2RAAECBAgQIECAAAECBAgQIECAQF8FFED7uvLmTYAAAQIECBAgQIAAAQIECBAgQKAHAgqgPVhkUyRAgAABAgQIECBAgAABAgQIECDQVwEF0L6uvHkTIECAAAECBAgQIECAAAECBAgQ6IGAAmgPFtkUCRAgQIAAAQIECBAgQIAAAQIECPRVQAG0rytv3gQIECBAgAABAgQIECBAgAABAgR6IKAA2oNFNkUCBAgQIECAAAECBAgQIECAAAECfRVQAO3ryps3AQIECBAgQIAAAQIECBAgQIAAgR4IKID2YJFNkQABAgQIECBAgAABAgQIECBAgEBfBRRA+7ry5k2AAAECBAgQIECAAAECBAgQIECgBwIKoD1YZFMkQIAAAQIECBAgQIAAAQIECBAg0FcBBdC+rrx5EyBAgAABAgQIECBAgAABAgQIEOiBgAJoDxbZFAkQIECAAAECBAgQIECAAAECBAj0VUABtK8rb94ECBAgQIAAAQIECBAgQIAAAQIEeiCgANqDRTZFAgQIECBAgAABAgQIECBAgAABAn0VUADt68qbNwECBAgQIECAAAECBAgQIECAAIEeCCiA9mCRTZEAAQIECBAgQIAAAQIECBAgQIBAXwUUQPu68uZNgAABAgQIECBAgAABAgQIECBAoAcCCqA9WGRTJECAAAECBAgQIECAAAECBAgQINBXAQXQvq68eRMgQIAAAQIECBAgQIAAAQIECBDogYACaA8W2RQJECBAgAABAgQIECBAgAABAgQI9FVAAbSvK2/eBAgQIECAAAECBAgQIECAAAECBHogoADag0U2RQIECBAgQIAAAQIECBAgQIAAAQJ9FVAA7evKmzcBAgQIECBAgAABAgQIECBAgACBHggogPZgkU2RAAECBAgQIECAAAECBAgQIECAQF8FFED7uvLmTYAAAQIECBAgQIAAAQIECBAgQKAHAgqgPVhkUyRAgAABAgQIECBAgAABAgQIECDQVwEF0L6uvHkTIECAAAECBAgQIECAAAECBAgQ6IGAAmgPFtkUCRAgQIAAAQIECBAgQIAAAQIECPRVQAG0rytv3gQIECBAgAABAgQIECBAgAABAgR6IKAA2oNFNkUCBAgQIECAAAECBAgQIECAAAECfRVQAO3ryps3AQIECBAgQIAAAQIECBAgQIAAgR4IKID2YJFNkQABAgQIECBAgAABAgQIECBAgEBfBRRA+7ry5k2AAAECBAgQIECAAAECBAgQIECgBwIKoD1YZFMkQIAAAQIECBAgQIAAAQIECBAg0FcBBdC+rrx5EyBAgAABAgQIECBAgAABAgQIEOiBgAJoDxbZFAkQIECAAAECBAgQIECAAAECBAj0VWBNXye+ivO+OufadkLn22tC4xqWAAECBAgQIECAAAECBAgQIECAQCcEFEAnv4x75hTutJ28szMQIECAAAECBAgQIECAAAECBAgQuJuAAujdSFp/4QkZ8f3JwQtGvjL7ty/43S4BAgQIECBAgAABAgQIECBAgAABAhMQUACdAOoWQ345vx+RfCp5dPPeqdke3+zbECBAgAABAgQIECBAgAABAgQIECAwIQGPZk8Idothf5Tffzm5uHn9t7N9UrNvQ4AAAQIECBAgQIAAAQIECBAgQIDAhAQUQCcEO2TYDXntxckdSbmvS3ZLNAIECBAgQIAAAQIECBAgQIAAAQIEJiSgADoh2EWG/du8/q7mvX2yffki/bxMgAABAgQIECBAgAABAgQIECBAgEALAgqgLSCOOUR99uelzTGvyvZeYx6vOwECBAgQIECAAAECBAgQIECAAAECIwr4EqQRoVrsdkPGekHyzGbMA7O9sNm3IUCAAAECBAgQIECAAAECBAgQIECgRQEF0BYxxxjqnPStaAQIECBAgAABAgQIECBAgAABAgQITFDAI/ATxDU0AQIECBAgQIAAAQIECBAgQIAAAQLTFVAAna6/sxMgQIAAAQIECBAgQIAAAQIECBAgMEEBBdAJ4hqaAAECBAgQIECAAAECBAgQIECAAIHpCvgM0On6j3v27XLA3gsOunzBvl0CBAgQIECAAAECBAgQIECAAAECBLYQUADdAmTGfz0s1/fVBde47YJ9uwQIECBAgAABAgQIECBAgAABAgQIbCHgEfgtQPxKgAABAgQIECBAgAABAgQIECBAgEB3BBRAu7OWZkKAAAECBAgQIECAAAECBAgQIECAwBYCHoHfAmTGfz0/13f/Gb9Gl0eAAAECBAgQIECAAAECBAgQIEBgZgQUQGdmKUa6kNvS66qReupEgAABAgQIECBAgAABAgQIECBAgMA2CqD+CEYRqG+fPyhp40uXdhzlhPoQIECAAAECBAgQIECAAAECBAgQaENAAbQNxe6PcWqmuLblae7T8niGI0CAAAECBAgQIECAAAECBAgQIHA3AQXQu5Gs+gtVCNwz2bnJTdlel2xIrknq92m3v8kFPDxp40uzfirj7JRcn2gECBAgQIAAAQIECBAgQIAAAQIECHRMYNfM52XJl5Mqcm7aSm7Ne3+fvCc5OmnjEfQMM9V2Xs5ec14/1atwcgIECBAgQIAAAQIECBAgQIDA7AusyyVWHaXtJ3Nnf+aucC4F9s5Vn5wsVfTcWkH0whxfhdB5bgqg87x6rp0AAQIECBAgQIAAAQIECBBYTQEF0Ba0PQLfAuIIQ+yRPmcnhy7oW4XOK5LLkquTjcnNSa1JfVHQbsl+yf7JDkm1Q5LTk1cnJyUaAQIECBAgQIAAAQIECBAgQIAAAQIEpiqwS85ej7sP7uw8N/vHJPdNRmn1DeyPS05JbkkG4xyV/Xls7gCdx1VzzQQIECBAgAABAgQIECBAgMA0BNwBOg115xxb4LgcMShafij7K/kioSp6DoqgF6xwrBw+laYAOhV2JyVAgAABAgQIECBAgAABAgTmUEABtIVFW0kxroXT92KIxzazrILlsckdK5j1mTn2Nc3x9Tj9gSsYy6EECBAgQIAAAQIECBAgQIAAAQIEOi+gADr5Ja7H16udkdS3uq+0fWzBAAcv2LdLgAABAgQIECBAgAABAgQIECBAgMAWAgqgW4BM4Nd9mzG/19LY12ScQSF1p5bGNAwBAgQIECBAgAABAgQIECBAgACBTgoogE5+WS9pTvGYlk5Vj9TXFyNV+9rmjZ8ECBAgQIAAAQIECBAgQIAAAQIECAwTUAAdptLua/WlP9Wenxx5597yf+yeQ9/RHH5ttpcufyhHEiBAgAABAgQIECBAgAABAgQIEOi+gALo5Nf4zTlFPbK+Y3Ja8pJk+2TcdngOOCupbbX3bt74SYAAAQIECBAgQIAAAQIECBAgQIDA/2/vTqClKcs7gQ/ysShRBBfcEFBwG4zbHJdoXGeMiktcgpmIWyaK0Wg0MSbqqIlGzWjUuOCoScYFjcZEM+4LR4/gNuo4gHqM4gIKyuKO7Mv3zf/RKi3vubdu9719q7v6/t5z/lR31VtVb/0Kiu7nVnevJbBjrQXmz0ygPgL/jOTFyb5JFS7r8fHJSUndxXl2cmFyUVLnpIqlV0kOTA5N7pwcnrStCqHPap+YEiBAgAABAgQIECBAgAABAgQIECBAYN4Cj84ALkh2bTIfyPr7J2Nt9ZUAZfDOsR6AcRMgQIAAAQIECBAgQIAAAQIEBhI4NvupOspRA+1vKXfjI/DDndbXZ1cHJS9Izppytxenf318/n7JvZP6/k+NAAECBAgQIECAAAECBAgQIECAAIF1BHwEfh2gGS/+Xrb3zCYHZ3r75LCkPu5eH4+/clLfF3pecm5SH5//cnJyUvM0AgQIECBAgAABAgQIECBAgAABAgSmEFAAnQJrxl1Py/YqGgECBAgQIECAAAECBAgQIECAAAECWyTgI/BbBGuzBAgQIECAAAECBAgQIECAAAECBAjMX8AdoPM/B6uN4GmZeetmwRMzrY/OawQIECBAgAABAgQIECBAgAABAgQITCngDtApwQbq/pvZz0Ob7DPQPu2GAAECBAgQIECAAAECBAgQIECAwNIJKIAu3Sl1QAQIECBAgAABAgQIECBAgAABAgQItAIKoK2EKQECBAgQIECAAAECBAgQIECAAAECSyegALp0p9QBESBAgAABAgQIECBAgAABAgQIECDQCiiAthKmBAgQIECAAAECBAgQIECAAAECBAgsnYAC6NKdUgdEgAABAgQIECBAgAABAgQIECBAgEAroADaSpgSIECAAAECBAgQIECAAAECBAgQILB0AjuW7oiW44B25jAuaw5l13IckqMgQIAAAQIECBAgQIAAAQIECBAgMLyAAujw5pPs8QGTdNKHAAECBAgQIECAAAECBAgQIECAAIF+AR+B7/exlAABAgQIECBAgAABAgQIECBAgACBEQsogI745Bk6AQIECBAgQIAAAQIECBAgQIAAAQL9Agqg/T6WEiBAgAABAgQIECBAgAABAgQIECAwYgEF0BGfPEMnQIAAAQIECBAgQIAAAQIECBAgQKBfQAG038dSAgQIECBAgAABAgQIECBAgAABAgRGLKAAOuKTZ+gECBAgQIAAAQIECBAgQIAAAQIECPQLKID2+1hKgAABAgQIECBAgAABAgQIECBAgMCIBRRAR3zyDJ0AAQIECBAgQIAAAQIECBAgQIAAgX4BBdB+H0sJECBAgAABAgQIECBAgAABAgQIEBixgALoiE+eoRMgQIAAAQIECBAgQIAAAQIECBAg0C+gANrvYykBAgQIECBAgAABAgQIECBAgAABAiMWUAAd8ckzdAIECBAgQIAAAQIECBAgQIAAAQIE+gUUQPt9LCVAgAABAgQIECBAgAABAgQIECBAYMQCCqAjPnmGToAAAQIECBAgQIAAAQIECBAgQIBAv4ACaL+PpQQIECBAgAABAgQIECBAgAABAgQIjFhAAXTEJ8/QCRAgQIAAAQIECBAgQIAAAQIECBDoF1AA7fexlAABAgQIECBAgAABAgQIECBAgACBEQsogI745Bk6AQIECBAgQIAAAQIECBAgQIAAAQL9Agqg/T6WEiBAgAABAgQIECBAgAABAgQIECAwYgEF0BGfPEMnQIAAAQIECBAgQIAAAQIECBAgQKBfQAG038dSAgQIECBAgAABAgQIECBAgAABAgRGLKAAOuKTZ+gECBAgQIAAAQIECBAgQIAAAQIECPQLKID2+1hKgAABAgQIECBAgAABAgQIECBAgMCIBRRAR3zyDJ0AAQIECBAgQIAAAQIECBAgQIAAgX4BBdB+H0sJECBAgAABAgQIECBAgAABAgQIEBixgALoiE+eoRMgQIAAAQIECBAgQIAAAQIECBAg0C+gANrvYykBAgQIECBAgAABAgQIECBAgAABAiMWUAAd8ckzdAIECBAgQIAAAQIECBAgQIAAAQIE+gUUQPt9LCVAgAABAgQIECBAgAABAgQIECBAYMQCCqAjPnmGToAAAQIECBAgQIAAAQIECBAgQIBAv4ACaL+PpQQIECBAgAABAgQIECBAgAABAgQIjFhAAXTEJ8/QCRAgQIAAAQIECBAgQIAAAQIECBDoF1AA7fexlAABAgQIECBAgAABAgQIECBAgACBEQsogI745Bk6AQIECBAgQIAAAQIECBAgQIAAAQL9Agqg/T6WEiBAgAABAgQIECBAgAABAgQIECAwYgEF0BGfPEMnQIAAAQIECBAgQIAAAQIECBAgQKBfQAG038dSAgQIECBAgAABAgQIECBAgAABAgRGLKAAOuKTZ+gECBAgQIAAAQIECBAgQIAAAQIECPQLKID2+1hKgAABAgQIECBAgAABAgQIECBAgMCIBRRAR3zyDJ0AAQIECBAgQIAAAQIECBAgQIAAgX4BBdB+H0sJECBAgAABAgQIECBAgAABAgQIEBixgALoiE+eoRMgQIAAAQIECBAgQIAAAQIECBAg0C+gANrvYykBAgQIECBAgAABAgQIECBAgAABAiMWUAAd8ckzdAIECBAgQIAAAQIECBAgQIAAAQIE+gUUQPt9LCVAgAABAgQIECBAgAABAgQIECBAYMQCCqAjPnmGToAAAQIECBAgQIAAAQIECBAgQIBAv4ACaL+PpQQIECBAgAABAgQIECBAgAABAgQIjFhAAXTEJ8/QCRAgQIAAAQIECBAgQIAAAQIECBDoF9jRv9jSLRTYK9u+eAPbv1rWuWKz3hkbWN8qBAgQIECAAAECBAgQIECAAAECBLaNgDtAhz3VD8nuPpCcnVyY/HvypuSOyaTtDel4epNJ19GPAAECBAgQIECAAAECBAgQIECAwLYUUAAd5rTvk928MfmX5F7JNZPdkpskD09OSF6atHd25qFGgAABAgQIECBAgAABAgQIECBAgMBmBRRANys42fovSLdHdLqen8enJruaeXUenpKclBzSzDMhQIAAAQIECBAgQIAAAQIECBAgQGCTAgqgmwScYPVbps8Tmn710fcHJFdJbpDslzwt+UlS7UbJxxJF0CBoBAgQIECAAAECBAgQIECAAAECBDYroAC6WcH11//DdNk9uSz5reTdyc6kWhU+X5zcNDk5qXb95CPJAfVEI0CAAAECBAgQIECAAAECBGYmUD9IrBEgsM0EFEC3/oRXcbPaPyVtkfNnMzr/ODOP75wc38yrO0Dfl9R3h2oECBAgQIAAAQIECBAgQIDAxgSuntWenXw+uSC5KDk3qfffT0yumGgECBAgsEmBs7N+fdfnkybYTl14P9X0r3WqCFp3j3bbe/KklrXfH9pdNobH9T+dGvs7xzBYYyRAgAABAgQIECBAgACB0Qo8OiOvT16276FrWgXQ7vPT8/zuiUZgUQWOzcDq39mjFnWAYxiXO0C3/izt2eyi/tK0XrswHe6ffL3peJ9MX9k8NiFAgAABAgQIECBAgAABAgQmE3hWuv2vpH6D471JfSVdfcpy72S/5Mjkc8n1kg8lv5NoBAgQILBBgc9mvarUv3SK9W+Yvuc069W6f9JZ1x2gHQwPCRAgQIAAAQIECBAgQIDACoHfzvN6L31p8sgVy7pPd8uT5yfVt25aOjzRCCyagDtAF+2MGM+qAm/J3LqY1kfh91+1x+ozb5/ZdQGudXcmj0iqKYD+3ME/CRAgQIAAAQIECBAgQIDASoH6FOapSb2XftLKhWs8//umf90JqhFYNAEF0EU7I8azqsARmVsX3soHk2l+3f2B6X95s25Nn5PU94K228vD0TXfATq6U2bABAgQIECAAAECBAgQGI1Ae/fnFzPiSb/2rz4S/+Ok3mvXJzI1AoskoAC6SGfDWHoFjsvStmj5wzx+ffJHvWv8cuHReVh3gLbrtwXRej7GpgA6xrNmzAQIECBAgAABAgQIEBiHwGsyzHq//LQph9sWmSZ9rz7l5nUnsGGB9t9NP4K0YcLJ/xqyiV1YNQJVxKy/PlWrvyw9KnlcMkl7bTr9fnJZ03nSv2BNsm19CBAgQIAAAQIECBAgQIDAMgkc3BzMyVMe1ElN/3b9KVfXnQCBRRZQTBvm7Hwzu7ltckxyfrPL7zbTSSZvSKdbJR+fpLM+BAgQIECAAAECBAgQIEBgmwrs1Rz3xVMef9u/XX/K1XUnQGCRBRRAhzs7F2VXdSv9VZM7JH+bTNO+lM53Th6Z/J/k3EQjQIAAAQIECBAgQIAAAQIEfinQ3mx0w1/OmujRoU2v70zUWycCBEYloAA6/Omqj7JXAfPDG9z1m7JeFVD33eD6ViNAgAABAgQIECBAgAABAssqcHxzYA+c4gB3T9/7N/1PmGI9XQkQGImAAuhITpRhEiBAgAABAgQIECBAgAABAusK/Ft61FfPHZHcad3eP+/wmEwOSb6e1A1LGgECSyagALpkJ9ThECBAgAABAgQIECBAgACBbSzwvRx7+5Vzb8/jG61jcbcsf1nT5y8y3blOf4sJECBAYIsF9sj2r9fJFu9uSzb/+Wx1V/LOLdm6jRIgQIAAAQIECBAgQIDAdhfYEYDjknrv+aPk8cneSbftlyfPTS5Jqt8rE43AIgocm0HVv6NHLeLgjInAVgjcJhutf+nbbMU+tnqbCqBbLWz7BAgQIECAAAECBAgQIHClENQdoO375/Py+GNJ3Yzz6aQtfNbyFyY+IRsEbSEFFEAX8rQY1FYKKIBupa5tEyBAgAABAgQIECBAgMCyCdSPG1XBsz7a3hZDa1oF0Pcnt0s0AossoAA6g7NTt4VrBAgQIECAAAECBAgQIECAAIFlFHh3DqpyreQmSX30/ZzkS8lPEo0AgW0goAA6rpN8coZbF22NAAECBAgQIECAAAECBAgQmFzgrHStaAQIbEMBBdBxnfTLMtyzxzVkoyVAgAABAgQIECBAgAABAgQIECAwPwEF0PnZj2nPd8tgH5bM4kuhD2oOfK8xARgrAQIECBAgQIAAAQIECBAgQIDAOAUUQMd53oYe9ZOzw/ri6Fm2q81yY7ZFgAABAgQIECBAgAABAgQIECBAYDUBBdDVVIadd53sbv/kSk0uyrS+iPnc5AdJPZ93e0IG8G/JbjMYSN1Jeo/kHTPYlk0QIECAAAECBAgQIECAAAECBAgQ6BVQAO3l2ZKFV85WH5FUIfDwpJ6v1eo7P7+YfCZ5b/L+ZFcydDsjO3zDjHb669lOFUAvndH2bIYAAQIECBAgQIAAAQIECBAgQIDAmgKz+E7HNTduwa8IHJBnxyTfSV6V3CHpK35m8X+oAvWtksclVQD9QnJEohEgQIAAAQIECBAgQIAAAQIECBAgMIGAO0AnQJpBl/2yjeOSm3e2VXdynpl8O/lecmFycVLnZO/kKsmBSf1oUPuDQXXH6LuTP03+LtEIECBAgAABAgQIECBAgAABAgQIEOgRUADtwZnRon2ynfclbfHzc3n80uQjSRU+12t7pMNtk/rY/KOTev6y5JSkPhKvESBAgAABAgQIECBAgAABAgQIECBAYG4CVbSsuz0rb00287UD98n6lzTbqo/Db2ZbWX0urYq3ZVG/LK8RIECAAAECBAgQIECAAAECBAisLXBsFlUd5ai1u1iynsAYC2jrHdOiLf+NZkBVsKy7OHduYoB1x+dTm/XrjtJDNrEtqxIgQIAAAQIECBAgQIAAAQIECBBYegEF0K0/xXdsdvGeTGfxy+fv6Az5Rp3HHhIgQIAAAQIECBAgQIAAAQIECBAgsEJAAXQFyBY8vV6zzdNntO0fZDttIfWKM9qmzRAgQIAAAQIECBAgQIAAAQIECBBYSgEF0K0/rd9odnGHGe2qPlJfP4RU7cSfT/yTAAECBAgQIECAAAECBAgQIECAAIHVBBRAV1OZ7bzPN5t7aKZ32eSmr5r1X9Js44eZnrrJ7VmdAAECBAgQIECAAAECBAgQIECAwFILKIBu/el9YXZRH1nfO3lXcnSyZzJtu2VW+HBS02qv+fnEPwkQIECAAAECBAgQIECAAAECBAgQWEtgx1oLzJ+ZQH0E/hnJi5N9kypc1uPjk5OSuovz7OTC5KKkzkkVS6+SHJgcmtw5OTxpWxVCn9U+MSVAgAABAgQIECBAgAABAgQIECBAYHUBBdDVXWY992+zwfrxomOS+uGiKyf3bZLJVO2D6f2wZOdUa+lMgAABAgQIECBAgAABAgQIECBAYBsK+Aj8cCf99dnVQckLkrOm3O3F6V8fn79fcu+kvv9TI0CAAAECBAgQIECAAAECBAgQIEBgHQF3gK4DNOPF38v2ntnk4ExvnxyW1Mfd6+PxdWdofV/oecm5SX18/svJyUnN0wgQIECAAAECBAgQIECAAAECBAgQmEJAAXQKrBl3PS3bq2gECBAgQIAAAQIECBAgQIAAAQIECGyRgALoFsFucrNPy/q3brbxxEzrzlGNAAECBAgQIECAAAECBAgQIECAAIEpBXwH6JRgA3X/zeznoU32GWifdkOAAAECBAgQIECAAAECBAgQIEBg6QQUQJfulDogAgQIECBAgAABAgQIECBAgAABAgRaAQXQVsKUAAECBAgQIECAAAECBAgQIECAAIGlE1AAXbpT6oAIECBAgAABAgQIECBAgAABAgQIEGgFFEBbCVMCBAgQIECAAAECBAgQIECAAAECBJZOQAF06U6pAyJAgAABAgQIECBAgAABAgQIECBAoBVQAG0lTAkQIECAAAECBAgQIECAAAECBAgQWDqBHUt3RMtxQDtzGJc1h7JrOQ7JURAgQIAAAQIECBAgQIAAAQIECBAYXkABdHjzSfb4gEk66UOAAAECBAgQIECAAAECBAgQIECAQL+Aj8D3+1hKgAABAgQIECBAgAABAgQIECBAgMCIBRRAR3zyDJ0AAQIECBAgQIAAAQIECBAgQIAAgX4BBdB+H0sJECBAgAABAgQIECBAgAABAgQIEBixgALoiE+eoRMgQIAAAQIECBAgQIAAAQIECBAg0C+gANrvYykBAgQIECBAgAABAgQIECBAgAABAiMWUAAd8ckzdAIECBAgQIAAAQIECBAgQIAAAQIE+gUUQPt9LCVAgAABAgQIECBAgAABAgQIECBAYMQCCqAjPnmGToAAAQIECBAgQIAAAQIECBAgQIBAv4ACaL+PpQQIECBAgAABAgQIECBAgAABAgQIjFhAAXTEJ8/QCRAgQIAAAQIECBAgQIAAAQIECBDoF1AA7fexlAABAgQIECBAgAABAgQIECBAgACBEQsogI745Bk6AQIECBAgQIAAAQIECBAgQIAAAQL9Agqg/T6WEiBAgAABAgQIECBAgAABAgQIECAwYgEF0BGfPEMnQIAAAQIECBAgQIAAAQIECBAgQKBfQAG038dSAgQIECBAgAABAgQIECBAgAABAgRGLKAAOuKTZ+gECBAgQIAAAQIECBAgQIAAAQIECPQLKID2+1hKgAABAgQIECBAgAABAgQIECBAgMCIBRRAR3zyDJ0AAQIECBAgQIAAAQIECBAgQIAAgX4BBdB+H0sJECBAgAABAgQIECBAgAABAgQIEBixgALoiE+eoRMgQIAAAQIECBAgQIAAAQIECBAg0C+gANrvYykBAgQIECBAgAABAgQIECBAgAABAiMWUAAd8ckzdAIECBAgQIAAAQIECBAgQIAAAQIE+gUUQPt9LCVAgAABAgQIECBAgAABAgQIECBAYMQCCqAjPnmGToAAAQIECBAgQIAAAQIECBAgQIBAv4ACaL+PpQQIECBAgAABAgQIECBAgAABAgQIjFhAAXTEJ8/QCRAgQIAAAQIECBAgQIAAAQIECBDoF1AA7fexlAABAgQIECBAgAABAgQIECBAgACBEQvsGPHYDZ0AAQIECGxU4KCs+Mjkt5J6vHvyneSjybHJFxONAAECBAgQIECAAAECBJZAQAF0CU6iQyBAgACBiQWq0Pnc5E+TvVasda08v02z7I2ZPjE5P9EIECBAgAABAgQIECBAYMQCPgI/4pNn6AQIECAwlUD90e9dyTOSPZI3J/dKrpdcO7lL8srk0uTRySeSqyYaAQIECBAgQIAAAQIECBAgQGBigZel567kyROvoSMBAgRmI/CKbKauP2cnd+zZ5I2y7CtJ9f1gTz+LCBAgQIAAAQIECBAgsNUC9RVd9d7kqK3e0TJv3x2gy3x2HRsBAgQItAK3yIMnJBcnRySfTNZqp2TBf07OSeo7Qh+caAQIECBAgAABAgQIECAwUgEF0JGeOMMmQIAAgakE/ji96/95r0r+7wRrnpE+/73p95QJ+utCgAABAgQIECBAgAABAgsqoAC6oCfGsAgQIEBgpgJ112e1f/j5ZKJ/viW9LkzukOw/0Ro6ESBAgAABAgQIECBAgMDCCSiALtwpMSACBAgQmLHAr2V710zOS+q7PSdtF6Tjl5P6f+Uhk66kHwECBAgQIECAAAECBAgsloAC6GKdD6MhQIAAgdkL7NNs8vwNbLpdp93GBjZhFQIECBAgQIAAAQIECBCYp4AC6Dz17ZsAAQIEhhD4fnZyeXL15EpT7vCgpv+ZU66nOwECBAgQIECAAAECBAgsiIAC6IKcCMMgQIAAgS0TqOLnZ5Ldk3tPsZfD07cKoPVr8N+YYj1dCRAgQIAAAQIECBAgQGCBBBRAF+hkGAoBAgQIbJnA25ot1y+775hwL3/V9Ht7pjsnXEc3AgQIECBAgAABAgQIEFgwAQXQBTshhkOAAAECWyLwumz1tOSWyTHJbklfe2oWPiip7wB9QV9HywgQIECAAAECBAgQIEBgsQUUQBf7/BgdAQIECMxG4OJs5sjkouSxyfuSw5KV7YDM+Mfkxcmu5FGJ7/8MgkaAAAECBAgQIECAAIGxCkz6McCxHp9xEyBAgACBVuBzeVDfAfqvzfRemdZ3g34puSy5UfKbyR5JFUr/IKm+GgECBAgQIECAAAECBAiMWEABdMQnz9AJECBAYGqBj2WNmyfPSR6e3L5JJj9rl+afVfSs7wr96s/m+AcBAgQIDCmwb3Z2j+TgZK/kO8kJyWmJRoAAAQIECBDYkIAC6IbYrESAAAECIxaoj7Q/LnlKUnd8Xj+p/x+ekXwi+XGiESBAgMCwAtfL7p6XPCypO/FXtro+/3nyqZULPCdAgAABAgQIrCdQb/g0AgQIECCwHQUuzEF/eDseuGMmQIDAggncLeOpu+/3T+orST6SnJzU9zcfmtwzuVPy8eSZyd8kGgECBAgQIECAAIGFFXhZRlY/LPLkhR2hgREgQIAAAQIECAwlcJvs6IKkXh++Jzk4Wdn2yYy6O/TyxOvIlTqeEyBAgMCyCxybA6z//x217Afq+Agsk4AC6DKdTcdCgAABAgQIENi4QH3U/ZSk3tT9fbJb0teOzMKdSd0lerO+jpYRIECAAIElElAAncHJvMIMtmETBAgQIECAAAECBAgQmFbgEVnhsOTLyeOTKoT2tbdn4THJ7slfJhoBAgQIECBAYCIBBdCJmHQiQIAAAQIECBAgQGDGAg9ttlff6XnphNt+fvrVXaD3Ta404Tq6ESBAgAABAttcQAF0m/8L4PAJECBAgAABAgQIzEngts1+PzDF/s9K3xOTKya/PsV6uhIgQIAAAQLbWEABdBuffIdOgAABAgQIECBAYE4Ce2e/+yYXJd+fcgxnNP0PmHI93QkQIECAAIFtKqAAuk1PvMMmQIAAAQIECBAgMEeBi7PvS5K9kj2nHMdVmv4/nXI93QkQIECAAIFtKqAAuk1PvMMmQIAAAQIECBAgMEeB+sGjryX1y++3m2Ic9cvxt2761/oaAQIECBAgQGBdAQXQdYl0IECAAAECBAgQIEBgCwTe22zz6Cm2/bvpWx+dPyk5fYr1dCVAgAABAgS2sYAC6DY++Q6dAAECBAgQIECAwBwFjsm+6ztAfy85YoJxXCd9/kfT7yUT9NeFAAECBAgQIPAzAQVQ/yIQIECAAAECBAgQIDAPgbqD8zlJfQz+n5OHJGu1m2TBR5NrJx9J3pJoBAgQIECAAIGJBHZM1EsnAgQIECBAgAABAgQIzF7gRdnkDZL6GPy/JMclb0rqI+71I0k3TB6YPCqp7/88MfmdpL5DVCNAgAABAgQITCSgADoRk04ECBAgQIAAAQIECGyRwOOy3S8kf538lyaZ/Eq7PM9elzwlueBXlnhCgAABAgQIEFhHQAF0HSCLCRAgQIAAAQIECBDYcoFXZw9vTf5rcq/kkGTP5LvJ8Ukt+2qiESBAgAABAgSmFlAAnZrMCgQIECBAgAABAgQIbIHAj7LNKoRWNAIECBAgQIDAzAT8CNLMKG2IAAECBAgQIECAAAECBAgQIECAAIFFE1AAXbQzYjwECBAgQIAAAQIECBAgQIAAAQIECMxMQAF0ZpQ2RIAAAQIECBAgQIAAAQIECBAgQIDAogkogC7aGTEeAgQIECBAgAABAgQIECBAgAABAgRmJqAAOjNKGyJAgAABAgQIECBAgAABAgQIECBAYNEEFEAX7YwYDwECBAgQIECAAAECBAgQIECAAAECMxNQAJ0ZpQ0RIECAAAECBAgQIECAAAECBAgQILBoAgqgi3ZGjIcAAQIECBAgQIAAAQIECBAgQIAAgZkJKIDOjNKGCBAgQIAAAQIECBAgQIAAAQIECBBYNAEF0EU7I8ZDgAABAgQIECBAgAABAgQIECBAgMDMBBRAZ0ZpQwQIECBAgAABAgQIECBAgAABAgQILJqAAuiinRHjIUCAAAECBAgQIECAAAECBAgQIEBgZgI7ZrYlGyIwncDT0/3o6VbRexMC+2Td6yaXJzs3sR2rEiCwvAK75dDqdYHrxPKeY0dGYLMCrhObFbQ+geUXaK8T5+RQf7z8h+sICQwicJ1B9rLkO1EAXfITvICHd1ozpmtmWtGGFXDX97De9kZgjAKuE2M8a8ZMYFgB14lhve2NwBgFrpVBVzQCBGYjsCub+dZsNrU9t1J/ndEIDC1ww+xwj6F3us33d2SO/6+S9yev2uYWDp8AgdUF7p/Zj0velbx29S7mEiCwzQUenOP/b8k7kn/c5hYOnwCB1QUemtmPTF6TvHz1LuYSILABgfOyzhkbWM8qjYA7QP2rMA+Bb8xjp9t8n2c3x396ph/Y5hYOnwCB1QUOa2bXX5ZdJ1Y3MpfAdhc4vAE4NVPXie3+b4PjJ7C6wK2b2T/I9CurdzGXAAECwwv4+Mrw5vZIgAABAgQIECBAgAABAgQIECBAgMBAAgqgA0HbDQECBAgQIECAAAECBAgQIECAAAECwwsogA5vbo8ECBAgQIAAAQIECBAgQIAAAQIECAwkoAA6ELTdECBAgAABAgQIECBAgAABAgQIECAwvIAC6PDm9kiAAAECBAgQIECAAAECBAgQIECAwEACCqADQdsNAQIECBAgQIAAAQIECBAgQIAAAQLDCyiADm9ujwQIECBAgAABAgQIECBAgAABAgQIDCSgADoQtN0QIECAAAECBAgQIECAAAECBAgQIDC8gALo8Ob2SIAAAQIECBAgQIAAAQIECBAgQIDAQAIKoANB2w0BAgQIECBAgAABAgQIECBAgAABAsMLKIAOb26PBAgQIECAAAECBAgQIECAAAECBAgMJKAAOhC03RAgQIAAAQIECBAgQIAAAQIECBAgMLyAAujw5vZIgAABAgQIECBAgAABAgQIECBAgMBAAgqgA0HbDQECBAgQIECAAAECBAgQIECAAAECwwsogA5vbo8ECBAgQIAAAQIECBAgQIAAAQIECAwkoAA6ELTdECBAgAABAgQIECBAgAABAgQIECAwvIAC6PDm9khgHgLnNjv9yTx2bp8ECIxCoL1OtNNRDNogCRAYVKB9HdFOB925nREgMAqB9nWE68QoTpdBEiBAgACB5RLYPYdz3+TKy3VYjoYAgRkK7Mi26jqxzwy3aVMECCyXwB45nPslV1quw3I0BAjMUGDPbKuuE3vPcJs2RYAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJLIXDDHMU/JCcm5yZfbp4/OtN9klm2I7KxtySfTX6UnJ2ckLw2uWWiESCwmAJDXidWE3h8Zp7V5NDVOphHgMDcBYa8TtwmR/vc5P1JvZaoHJ88P9k30QgQWEyBoa4Te+fwn558IDk1+Wny/5J6H3L3RCNAgAABAgS2mcBTc7yXJLvWyKcyf79ks+0G2cBxyVr7qfmXJS9PZl10zSY1AgQ2ITDUdWKtId4sCy5M2uvHTdbqaD4BAnMTGPI68cQcZd9rl3OyvP7gqhEgsFgCQ10n7pLD/kbSvm5YbfrmLPfHksX698NoCBAgQIDAlgnUHZ7tC4IqLrwhOTr56+SkpF32hTw+INloq7/A1jba7dVdGi9N/iB5UvLG5NKkXV7PNQIEFkNgqOvEWke7ZxbU3ent9aGmCqBraZlPYD4CQ10ndsvhvSlprwcX5/H7ksclf5bUH23bZXW3140TjQCBxRAY6jpxYA63PmXWXgvqU2d1fTgq+Zvkx0m77J/zWCNAgAABAgSWXOAaOb4LknoBUC8E7pJ02x558takfYFwTHfhlI9f1dnOB/N4/1XWv0XmndXp95BV+phFgMCwAkNeJ9Y6shdlQXsdaqcKoGtpmU9geIEhrxO/n8NrrwNfzePrrjjcK+R595pxworlnhIgMB+BIa8T9ZH39jpR7192X3HI18nzb3b6/O6K5Z4SIECAAAECSyZQ35HVvjiouz5Xa/VGov5qWv3qToorJ9O2HVnhvKS28cOk707S+zf9qm+9eNEIEJivwFDXibWO8q5ZcHlS14T6fuKaVhRAg6ARWBCBoa4Te+V4v5fUNeD85PrJaq2KHVUcrX51/ajCi0aAwHwFhrxOtF+P8e0ccn2KZLV278xsX1O8bbUO5hEgQIAAAQLLI3BmDqX+x19FhbVeHNTR1l9F2xcIT6gZU7bbp3+7/uvXWbcKrm2xtD4mrxEgMF+Boa4Tqx3lVTOz3rzU9aPuHK83KO215MZ5rBEgsBgCQ10nHpjDba8Bz1vn0OuHT05J6iPxd1ynr8UECGy9wFDXifpxtPY60ffx9iumX/32QPX9WqIRIECAAAECSypwcI6rfXHwnnWOse6c2Nn0rzcS07Z7ZoUPJ19K/miClduPpNQ+95qgvy4ECGyNwMHZ7FDXidWO4K3N/n+QaX1crX1eY7pxohEgMH+BgzOEoa4T/9TZV/2KtEaAwDgEDs4wh7pOdAugfZ8mqx9cbT9h8q1xMBolAQIECBAgsBGB7l2d691FUdv/TlIvXOpu0a1s9UuMbbH137dyR7ZNgMC6AvO8Tjwso2vfLB3ZjFQBdN1TpgOBwQWGvE60H2tXrBj8NNshgU0JDHmd+LWMtL4io15D1A8hXT1ZrdVri/Z1xrtW62AeAQIEphWoj7NqBAg59eFYAAAVZ0lEQVQsnsBhnSGd2nm81sP6GGq1+g7QuhNrq9pjs+H6hddq9d2jGgEC8xOY13XioBzyMc1hvyXTt8+PwJ4JEFhHYKjrRH1c9dBmLCc103qfcafkGckHk08mr0iq2OI9SBA0AgsiMNR1og63vkqrfQ1RX6VzbLJf0m11l+grmxl148WLuws9JkCAwEYF6sdPNAIEFk/gKp0hTfJdm/WjA23bPw++2z6Z4fTa2dYzm+3Vi5HXzXDbNkWAwPQC87hOVNHiTUndDX56MsnXZqSbRoDAnASGuk7UH0baomZ9LcYeSV0rqtjZbb+RJ09MHpM8Mjkj0QgQmK/AUNeJ9ijrjyL1vuKo5F5J3T1+XFLvX26a1Lzdk0uSo5NPJBoBAgQ2LaAAumlCGyCwJQJVXGjbhe2Dnmm3z5V6+m10UY2nvqenHdfL87ju5NAIEJifQPvfY42gew1Ya0TdPhu9TvxZNn7nZFfyqOTHiUaAwOIKDHWdqE+gtO2iPHh3UkWM+hGTLyf1IyZ1l9nNknr/cffkxOTmyVmJRoDA/ASGuk60R1jXhYcnxyevTa6R/F7SbefkyT2S+o0CjQABAjMRaP9SO5ON2QgBAjMTWPlGYr0NX9zpsNHCRmcTv/KwPtZW371zi2buKZm2d4I2s0wIEJiDwNDXiVvnGJ/XHGf9EeSjczhmuyRAYDqBoa4T3f3U3Z1V/KwCZ712qDykmd4q07agcfU8/rtEI0BgvgLd/37rDxjrtc2+79gvO6g/krwuaesR9QfVeo9RP3xU7ZpJFUgfX080AgQIzEKgveDMYlu2QYDA7AQu7Wxqkju1u30meeHS2Xzvw3pz8pHkLk2vb2dab2q6d5I1i0wIEBhYYMjrRP0h5C3JHkndzfX0RCNAYPEFhrpO7NmhqNck30nqtUNdL7qtip93S9q7xx+ax3VXuUaAwPwEhrpO1BHum5yQ3C+p3xX4RHLzpIqiN07q19/r6zF+mNTXetX3hXrNEQSNAIHNCyiAbt7QFghshcB5nY3u3Xm81sNun5+s1WnK+Yem/6eTOzTrnZrpXZOaagQIzF9gyOtE/QDBTZJ6k1Tf2TXLP7RkcxoBAlskMNR1orufOpQ/T366xjF9P/Nf2FmmANrB8JDAHAS6//1231OsNZRun2nfd/xJNnp4s+HjMq0/lHypeV6Turv0Tcltk3Zc9emTwxKNAAECmxJQAN0Un5UJbJnAuZ0td7+YvDP7Vx52+3TX/ZVOUzy5ffp+KqkiaLXPJ1UIVfwsDY3AYgh0/1vvXgPWGl23T3fdtfq38++dB09onrwk07oOXHWVdO8Aq321fepuMI0AgfkIdP9b714D1hpNt0933bX6t/NXFjtPaBesMf1kZ359L6hGgMD8BLr/rXevAWuNqNunu+5a/bvz29cTOzPzMUlNV2vfyMxnNwt2z/SPV+tkHgECBKYRUACdRktfAsMJ1P/023Zg+6Bn2vapLxX/QU+/SRY9MJ0+mtQXkld7f1J/nT27nmgECCyMwFDXift3jvgv8vhHa+RBnX6f7fS5Y2e+hwQIDCsw1HXijM5h1Z3i3eedRb94+PVfPPrlH1s7szwkQGBAgaGuE/Xe4mrNcdU14FvrHOMHO8vrY/IaAQIENiWgALopPisT2DKB7ndmtXdhrrWzPbLgoGbhFzPdzEdTj876/5rU9/1V+59JFT/OrycaAQILJTCv68RCIRgMAQK9AkNdJ+qPr2c2I6nXJTfsHdXPv++v7VJ/VNEIEJifwFDXibb4WUf63QkO95udPgd0HntIgACBDQn4WNqG2KxEYMsFTs4e6jtw9kruvM7ebtv0q26fWadv3+JHZWEVPOsLyXclT01emmgECCymwFDXiQ/k8Os7+9ZrdQdo+1HW1+Rxu856d3ist13LCRDYuMBQ14kaYb0G+e1mqPW1Od27PJvZv5gc9otHvl6nQ+EhgbkIDHWdqGtC+/7mNnlcH22/vOeIu39I+UpPP4sIECBAgACBkQv874y/CpGVW/Ucy2s7/Y7o6de3qL6MvD6yVvuqFyKPSDQCBBZfYMjrxHoab02H9pp14/U6W06AwGACQ10njswRtdeA9+Vx/UF1rfbOLGj73nutTuYTIDCYwFDXic/niNr/9tf7ipyndfo+ZzAJOyJAgAABAgQGF7hv9ti+QKjv07vqKiO4T+Zd0vSrj7+v9maj7vT+T53UR9NWtvqxgnZfz1650HMCBBZWYMjrxHoICqDrCVlOYD4CQ10n6pehT0va1xMvXONwu+OpO8TrLjCNAIH5CnT/u9zK9x31I0jtNeL0PD5kjcOuT5Rc0PS9MNObrNHPbAIECBAgQGBJBOqjp+2LhBPz+O5JvcG4bvKkpC1+1l2ba939eUCWtduoaa3bbXW3Z7u8tlN3bbx3wnS/yyeraAQIzEFgiOvEJIelADqJkj4E5iMw1HXinjm8y5L2dcWr8/iuSf0x9sDkGUl3efXXCBBYDIEhrhN1s8ZxSXuNODWPH5u0X4tx/Tx+SnJe0vbxC/DB0AgQIECAwLIL7J8D/FDSvgCoaVv07M57cg/EegXQT6/Yfne76z2+Xs9+LSJAYBiBIa4TkxyJAugkSvoQmI/AkNeJu+UQz0q6ryHqe/+6z+sPrn2vXbJYI0BgYIGhrhPXyXF9IuleE+px/ZBrd15dJ16RVNFUI0CAAAECBLaBwBVyjM9P6hdWuy8K6vEXkvoYfF9brwD6k6y8cruTPlcA7ZO3jMBwAlt9nZjkSBRAJ1HSh8D8BIa8Tlw7h1nfKXhusvI1xccz7x6JRoDA4gkMdZ2oombd+XlmsvIasTPzPpfcLtEIECAwMwF/TZkZpQ0RGETgkOylfhDpwuSU5NSkXiRoBAgQaAVcJ1oJUwIE1hIY6jpR7zVulNwiqWJovXb5ZqIRILD4AkNdJ64ZivrOz2slX0vqF9/PTzQCBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAIHtJbDb9jpcR0uAAAECBAgQILCNBfbLsT8/uUJj8OZMP9E8Xjk5NDOe2sy8PNNnJT9snpsQIECAAAECBAgQIECAAAECBAgQIEBgIQVelFHtanJqpvusMso9Mu+zTZ/q+4JV+phFgAABAgQIECBAgAABAgQIECBAgACBhRPYMyM6KWmLoK9YZYRV8GyXfyqPd6zSxywCBAgQIECAAAECBAgQIECAAAECBAgspMB/zKguTKrIuTO5U9K2u+RBfeS9lv0oOSjRCBAgQIAAAQIECBAgQIAAAQIECBAgMCqBJ2W0VeSsfCXZK9k3+XbSzn9wHmsECBAgQIAAAQIECBAgQIAAAQIECBAYnUD9GOiHkrbY+Zw8Prbz/NV5rBEgQIAAAQIECBAgQIAAAQIECBAgQGC0AtfOyL+fVBH00mZaj7+Q7J1oBAgQIECAAAECBAgQIECAAAECBAgQGLXAgzL69i7Qmp6f3HTUR2TwBAgQIECAAAECBAgQIECAAAECBAgQaAR2z/S0pC2CnpjHNU8jQIAAAQIECBAgQIAAAQIECBAgQIDA6AWenSNoi5/ttOZpBAgQIECAAAECBAgQIECAAAECBAgQGLXAbTP69rs/v5vHZyZVBK15tUwjQIAAAQIECBAgQIAAAQIECBAgQIDAKAX2yahPSdq7Pu+Xxw/sPK9l1UcjQIAAAQIECBAgQIAAAQIECBAgQIDA6ARelxG3xc9jO6N/W2d+9dEIECBAgAABAgQIECBAgAABAgQIECAwKoH7Z7Rt8bM++r5fZ/TXyONzOsurr0aAAAECBAgQIECAAAECBAgQIECAAIFRCByQUa5X4DwyfdoCafWtdTQCBAgQIECAAAECBAgQIECAAAECBAgsvMD7MsK2uNn96PvKgb+j06/W0QgQIECAAAECBAgQIECAAAECBAgQILDQAo/P6NriZ/3i+/49o627Pn/Q6f+HPX0tIkCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECyyfw/wE2HllE1zinJQAAAABJRU5ErkJggg==" title="plot of chunk unnamed-chunk-4" alt="plot of chunk unnamed-chunk-4" width="672" /></p>
<pre class="r"><code>sqrt(sum(e*e)/(length(e)-2))</code></pre>
<pre><code>## [1] 0.223</code></pre>
<pre class="r"><code>sd(e) * sqrt((length(e) - 1)/(length(e) - 2))</code></pre>
<pre><code>## [1] 0.223</code></pre>
</div>
<div id="question-3" class="section level3">
<h3>Question 3</h3>
<p>In the <code>mtcars</code> data set, fit a linear regression model of weight (predictor) on mpg (outcome). Get a 95% confidence interval for the expected mpg at the average weight. What is the lower endpoint?</p>
<ul>
<li>-4.00</li>
<li>21.190</li>
<li>-6.486</li>
<li>18.991</li>
</ul>
<pre class="r"><code>data(mtcars)
x = mtcars$wt
y = mtcars$mpg
# Easy way
fit <- lm(y ~ I(x - mean(x)))
coef <- summary(fit)$coefficients
coef[1,1] + -1 * qt(0.975, df = fit$df) * coef[1,2]</code></pre>
<pre><code>## [1] 18.99</code></pre>
</div>
<div id="question-4" class="section level3">
<h3>Question 4</h3>
<p>Refer to the previous question. Read the help file for mtcars. What is the weight coefficient interpreted as?</p>
<ul>
<li>The estimated expected change in mpg per 1 lb increase in weight.</li>
<li>The estimated 1,000 lb change in weight per 1 mpg increase.</li>
<li>The estimated expected change in mpg per 1,000 lb increase in weight.</li>
<li>It can’t be interpreted without further information</li>
</ul>
<pre class="r"><code>?mtcars</code></pre>
</div>
<div id="question-5" class="section level3">
<h3>Question 5</h3>
<p>Consider again the <code>mtcars</code> data set and a linear regression model with mpg as predicted by weight (1,000 lbs). A new car is coming weighing 3000 pounds. Construct a 95% prediction interval for its mpg. What is the upper endpoint?</p>
<ul>
<li>21.25</li>
<li>27.57</li>
<li>-5.77</li>
<li>14.93</li>
</ul>
<pre class="r"><code>mpg <- predict(fit, newdata = data.frame(x = 3))
mpg + qt(0.975, df = fit$df) * coef[2,2]</code></pre>
<pre><code>## 1
## 21.23</code></pre>
</div>
<div id="question-6" class="section level3">
<h3>Question 6</h3>
<p>Consider again the <code>mtcars</code> data set and a linear regression model with mpg as predicted by weight (in 1,000 lbs). A “short” ton is defined as 2,000 lbs. Construct a 95% confidence interval for the expected change in mpg per 1 short ton increase in weight. Give the lower endpoint.</p>
<ul>
<li>-6.486</li>
<li>-9.000</li>
<li>-12.973</li>
<li>4.2026</li>
</ul>
<pre class="r"><code>fit <- lm(y ~ I(x/2 - mean(x/2)))
coef <- summary(fit)$coefficients
coef[2,1] + -1 * qt(0.975, df = fit$df) * coef[2,2]</code></pre>
<pre><code>## [1] -12.97</code></pre>
</div>
<div id="question-7" class="section level3">
<h3>Question 7</h3>
<p>If my <span class="math">\(X\)</span> from a linear regression is measured in centimeters and I convert it to meters what would happen to the slope coefficient?</p>
<ul>
<li>It would get multiplied by 100 <–</li>
<li>It would get divided by 10</li>
<li>It would get multiplied by 10</li>
<li>It would get divided by 100</li>
</ul>
<pre class="r"><code>lm(y ~ x)</code></pre>
<pre><code>##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 37.29 -5.34</code></pre>
<pre class="r"><code>lm(y ~ I(x/100))</code></pre>
<pre><code>##
## Call:
## lm(formula = y ~ I(x/100))
##
## Coefficients:
## (Intercept) I(x/100)
## 37.3 -534.4</code></pre>
</div>
<div id="question-8" class="section level3">
<h3>Question 8</h3>
<p>I have an outcome, <span class="math">\(Y\)</span>, and a predictor, <span class="math">\(X\)</span> and fit a linear regression model with <span class="math">\(Y=\beta_0+\beta_1X+\epsilon\)</span> to obtain <span class="math">\(\hat\beta_0\)</span> and <span class="math">\(\hat\beta_1\)</span>. What would be the consequence to the subsequent slope and intercept if I were to refit the model with a new regressor, <span class="math">\(X+c\)</span> for some constant, <span class="math">\(c\)</span>?</p>
<ul>
<li>The new slope would be <span class="math">\(c\hat\beta_1\)</span></li>
<li>The new slope would be <span class="math">\(\hat\beta_1+c\)</span></li>
<li>The new intercept would be <span class="math">\(\hat\beta_0-c\beta_1\)</span> <–</li>
<li>The new intercept would be <span class="math">\(\hat\beta_0+c\hat\beta_1\)</span></li>
</ul>
<pre class="r"><code>l = lm(y ~ x)
lm(y ~ I(x + 10))</code></pre>
<pre><code>##
## Call:
## lm(formula = y ~ I(x + 10))
##
## Coefficients:
## (Intercept) I(x + 10)
## 90.73 -5.34</code></pre>
</div>
<div id="question-9" class="section level3">
<h3>Question 9</h3>
<p>Refer back to the mtcars data set with mpg as an outcome and weight (wt) as the predictor. About what is the ratio of the the sum of the squared errors, <span class="math">\(\sum_{i=1}^n(Y_i-\hat Y_i)^2\)</span> when comparing a model with just an intercept (denominator) to the model with the intercept and slope (numerator)?</p>
<ul>
<li>0.25 <–</li>
<li>0.75</li>
<li>0.50</li>
<li>4.00</li>
</ul>
<pre class="r"><code>modelA = mean(y)
modelB = lm(y ~ x)
sum((modelB$fitted.values - y)^2) / sum((modelA - y)^2)</code></pre>
<pre><code>## [1] 0.2472</code></pre>
</div>
<div id="question-10" class="section level3">
<h3>Question 10</h3>
<p>Do the residuals always have to sum to 0 in linear regression?</p>
<ul>
<li>The residuals never sum to zero.</li>
<li>The residuals must always sum to zero.</li>
<li>If an intercept is included, the residuals most likely won’t sum to zero.</li>
<li>If an intercept is included, then they will sum to 0. <–</li>
</ul>
<pre class="r"><code>modelC = lm(y ~ x - 1)
sum(modelC$fitted.values - y)</code></pre>
<pre><code>## [1] -98.12</code></pre>
</div>
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